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t,e,i=this.renderedQuestionArray.length;0!==i;)e=Math.floor(Math.random()*i),i-=1,t=this.renderedQuestionArray[i],this.renderedQuestionArray[i]=this.renderedQuestionArray[e],this.renderedQuestionArray[e]=t}async renderTimedQuestion(){if(this.currentQuestionIndex>=this.renderedQuestionArray.length)return;let t,e=this.renderedQuestionArray[this.currentQuestionIndex];if("prepared"===e.state||"forreview"===e.state||"broken_exam"===e.state&&e.initAttempts<3){let t=e.orig;if($(t).is("[data-component=selectquestion]"))if(this.done&&"prepared"==e.state)this.renderedQuestionArray[this.currentQuestionIndex].state="exam_ended";else{e.rqa=this.renderedQuestionArray;let t=new a.default(e);this.renderedQuestionArray[this.currentQuestionIndex]={question:t};try{await t.initialize(),"broken_exam"==e.state&&$(`ul#pageNums > ul > li:eq(${this.currentQuestionIndex})`).removeClass("broken")}catch(t){e.state="broken_exam",this.renderedQuestionArray[this.currentQuestionIndex]=e,console.log(`Error initializing question: Details ${t}`)}}else if($(t).is("[data-component]")){let i=$(t).data("component");this.renderedQuestionArray[this.currentQuestionIndex]={question:window.component_factory[i](e),state:e.state}}}else if("broken_exam"===e.state)return;t=this.renderedQuestionArray[this.currentQuestionIndex].question,"forreview"===e.state&&(await t.component_ready_promise,await t.checkCurrentAnswer(),t.renderFeedback(),t.disableInteraction()),this.visited.includes(this.currentQuestionIndex)||(this.visited.push(this.currentQuestionIndex),this.visited.length!==this.renderedQuestionArray.length||this.done||$(this.finishButton).show()),t.containerDiv&&(0==t.containerDiv.classList.contains("runestone")&&t.containerDiv.classList.add("runestone"),$(this.switchDiv).replaceWith(t.containerDiv),this.switchDiv=t.containerDiv),t.needsReinitialization&&t.reinitializeListeners(this.taken)}handlePrevAssessment(){$(this.startBtn).hide(),$(this.pauseBtn).attr("disabled",!0),$(this.finishButton).attr("disabled",!0),this.running=0,this.done=1,this.showResults&&this.showFeedback?($(this.timedDiv).show(),this.restoreAnsweredQuestions()):($(this.pauseBtn).hide(),$(this.timerContainer).hide())}startAssessment(){if(this.taken)this.handlePrevAssessment();else{if($("#relations-next").hide(),$("#relations-prev").hide(),$(this.startBtn).hide(),$(this.pauseBtn).attr("disabled",!1),0===this.running&&0===this.paused){this.running=1,this.lastTime=Date.now(),$(this.timedDiv).show(),this.increment(),this.logBookEvent({event:"timedExam",act:"start",div_id:this.divid});var t=new Date,e={answer:[0,0,this.renderedQuestionArray.length,0],timestamp:t};localStorage.setItem(this.localStorageKey(),JSON.stringify(e))}$(window).on("beforeunload",function(t){if(!this.done)return t.preventDefault(),t.returnValue="Are you sure you want to leave? Your work will be lost! And you will need your instructor to reset the exam!","Are you sure you want to leave? Your work will be lost!"}.bind(this)),window.addEventListener("pagehide",async function(t){this.done||(await this.finishAssessment(),console.log("Exam exited by leaving page"))}.bind(this))}}pauseAssessment(){0===this.done&&(1===this.running?(this.logBookEvent({event:"timedExam",act:"pause",div_id:this.divid}),this.running=0,this.paused=1,this.pauseBtn.innerHTML="Resume",$(this.timedDiv).hide()):(this.logBookEvent({event:"timedExam",act:"resume",div_id:this.divid}),this.running=1,this.paused=0,this.increment(),this.pauseBtn.innerHTML="Pause",$(this.timedDiv).show()))}showTime(){if(this.showTimer){var t=Math.floor(this.timeLimit/60),e=Math.floor(this.timeLimit)%60,i=t,s=e;t<10&&(i="0"+t),e<10&&(s="0"+e);var n="Time Remaining ";this.limitedTime||(n="Time Taken ");var r=n+i+":"+s;if(this.done||this.taken){var a=Math.floor(this.timeTaken/60),o=Math.floor(this.timeTaken%60);a<10&&(a="0"+a),o<10&&(o="0"+o),r="Time taken: "+a+":"+o}this.timerContainer.innerHTML=r;for(var h=document.getElementsByClassName("timeTip"),d=0;d<=h.length-1;d++)h[d].title=r}else $(this.timerContainer).hide()}increment(){1!==this.running||this.taken||setTimeout(function(){let t=Date.now();if(this.limitedTime?this.timeLimit=this.timeLimit-Math.floor((t-this.lastTime)/1e3):this.timeLimit=this.timeLimit+Math.floor((t-this.lastTime)/1e3),this.lastTime=t,localStorage.setItem(eBookConfig.email+":"+this.divid+"-time",this.timeLimit),this.showTime(),this.timeLimit>0)this.increment();else if($(this.startBtn).attr({disabled:"true"}),$(this.finishButton).attr({disabled:"true"}),this.running=0,this.done=1,!this.taken){this.taken=!0;let t=document.createElement("h1");t.innerHTML="Sorry but you ran out of time. Your answers are being submitted",this.controlDiv.appendChild(t),this.finishAssessment()}}.bind(this),1e3)}styleExamElements(){$(this.timerContainer).css({width:"50%",margin:"0 auto","background-color":"#DFF0D8","text-align":"center",border:"2px solid #DFF0D8","border-radius":"25px"}),$(this.scoreDiv).css({width:"50%",margin:"0 auto","background-color":"#DFF0D8","text-align":"center",border:"2px solid #DFF0D8","border-radius":"25px"}),$(".tooltipTime").css({margin:"0",padding:"0","background-color":"black",color:"white"})}async finishAssessment(){$("#relations-next").show(),$("#relations-prev").show(),this.showFeedback||($(this.timedDiv).hide(),$(this.pauseBtn).hide(),$(this.timerContainer).hide()),this.findTimeTaken(),this.running=0,this.done=1,this.taken=1,await this.finalizeProblems(),this.checkScore(),this.displayScore(),this.storeScore(),this.logScore(),$(this.pauseBtn).attr("disabled",!0),this.finishButton.disabled=!0,$(window).off("beforeunload");let t=this.divid;setTimeout((function(){jQuery.ajax({url:eBookConfig.app+"/assignments/student_autograde",type:"POST",dataType:"JSON",data:{assignment_id:t,is_timed:!0},success:function(t){0==t.success?console.log(t.message):console.log("Autograder completed")}})}),2e3)}async finalizeProblems(){var t=this.renderedQuestionArray[this.currentQuestionIndex].question;await t.checkCurrentAnswer(),await t.logCurrentAnswer(),t.renderFeedback(),t.disableInteraction();for(var e=0;e0?this.correctStr=this.correctStr.substring(0,this.correctStr.length-2):this.correctStr="None",this.skippedStr.length>0?this.skippedStr=this.skippedStr.substring(0,this.skippedStr.length-2):this.skippedStr="None",this.incorrectStr.length>0?this.incorrectStr=this.incorrectStr.substring(0,this.incorrectStr.length-2):this.incorrectStr="None"}findTimeTaken(){this.limitedTime?this.timeTaken=this.startingTime-this.timeLimit:this.timeTaken=this.timeLimit}storeScore(){var t=[];t.push(this.score,this.correctStr,this.incorrect,this.incorrectStr,this.skipped,this.skippedStr,this.timeTaken);var e=new Date,i=JSON.stringify({answer:t,timestamp:e});localStorage.setItem(this.localStorageKey(),i)}logScore(){this.logBookEvent({event:"timedExam",act:"finish",div_id:this.divid,correct:this.score,incorrect:this.incorrect,skipped:this.skipped,time_taken:this.timeTaken})}shouldUseServer(t){var e;if(0===localStorage.length)return!0;var i=localStorage.getItem(this.localStorageKey());if(null===i)return!0;try{var s=JSON.parse(i).answer;if(4==s.length){if(t.correct==s[0]&&t.incorrect==s[1]&&t.skipped==s[2]&&t.timeTaken==s[3])return!0}else if(7==s.length&&t.correct==s[0]&&t.incorrect==s[2]&&t.skipped==s[4]&&t.timeTaken==s[6])return!1;e=new Date(JSON.parse(i[1]).timestamp)}catch(t){return console.log(t.message),localStorage.removeItem(this.localStorageKey()),!0}return!(new Date(t.timestamp)0&&null!==localStorage.getItem(this.localStorageKey())?(this.taken=1,this.restoreAnswers("")):this.taken=0}async restoreAnswers(t){var e;if(this.taken=1,""===t){let t,i=!1;try{t=JSON.parse(localStorage.getItem(this.localStorageKey())),e=t.answer}catch(t){console.log(`Error parsing stored Timed data for ${this.divid}: ${t.message}`),i=!0}if(i||t.timestamp0||this.incorrectStr.length>0||this.skippedStr.length>0?(e=`Num Correct: ${this.score}. Questions: ${this.correctStr}
Num Wrong: ${this.incorrect}. Questions: ${this.incorrectStr}
Num Skipped: ${this.skipped}. Questions: ${this.skippedStr}
`,t=this.score+this.incorrect+this.skipped,e+="Percent Correct: "+(this.score/t*100).toFixed(2)+"%",$(this.scoreDiv).html(e),this.scoreDiv.style.display="block"):(e=`Num Correct: ${this.score}
Num Wrong: ${this.incorrect}
Num Skipped: ${this.skipped}
`,t=this.score+this.incorrect+this.skipped,e+="Percent Correct: "+(this.score/t*100).toFixed(2)+"%",$(this.scoreDiv).html(e),this.scoreDiv.style.display="block"),this.highlightNumberedList()}else $(this.scoreDiv).html("Thank you for taking the exam. Your answers have been recorded."),this.scoreDiv.style.display="block"}highlightNumberedList(){var t=this.correctStr,e=this.incorrectStr,i=this.skippedStr;t=t.replace(/ /g,"").split(","),e=e.replace(/ /g,"").split(","),i=i.replace(/ /g,"").split(","),$((function(){var s=$("ul#pageNums > ul > li");s.hasClass("answered")&&s.removeClass("answered");for(var n=0;n 1) this.renderNavControls();\n this.renderSubmitButton();\n this.renderFeedbackContainer();\n this.useRunestoneServices = eBookConfig.useRunestoneServices;\n // Replace intermediate HTML with rendered HTML\n $(this.origElem).replaceWith(this.containerDiv);\n // check if already taken and if so show results\n this.styleExamElements(); // rename to renderPossibleResults\n this.checkServer(\"timedExam\", true);\n }\n\n disableCutCopyPaste() {\n document.addEventListener(\"cut\", function (e) {\n e.preventDefault();\n });\n document.addEventListener(\"copy\", function (e) {\n e.preventDefault();\n });\n document.addEventListener(\"paste\", function (e) {\n e.preventDefault();\n });\n }\n\n renderContainer() {\n this.containerDiv = document.createElement(\"div\"); // container for the entire Timed Component\n if (this.fullwidth) {\n // allow the container to fill the width - barb\n $(this.containerDiv).attr({\n style: \"max-width:none\",\n });\n }\n this.containerDiv.classList.add(\"runestone-sphinx\");\n this.containerDiv.id = this.divid;\n this.timedDiv = document.createElement(\"div\"); // div that will hold the questions for the timed assessment\n this.navDiv = document.createElement(\"div\"); // For navigation control\n $(this.navDiv).attr({\n style: \"text-align:center\",\n });\n this.flagDiv = document.createElement(\"div\"); // div that will hold the \"Flag Question\" button\n $(this.flagDiv).attr({\n style: \"text-align: center\",\n });\n this.switchContainer = document.createElement(\"div\");\n this.switchContainer.classList.add(\"switchcontainer\");\n this.switchDiv = document.createElement(\"div\"); // is replaced by the questions\n this.timedDiv.appendChild(this.navDiv);\n this.timedDiv.appendChild(this.flagDiv); // add flagDiv to timedDiv, which holds components for navigation and questions for timed assessment\n this.timedDiv.appendChild(this.switchContainer);\n this.switchContainer.appendChild(this.switchDiv);\n $(this.timedDiv).attr({\n id: \"timed_Test\",\n style: \"display:none\",\n });\n }\n\n renderTimer() {\n this.wrapperDiv = document.createElement(\"div\");\n this.timerContainer = document.createElement(\"P\");\n this.wrapperDiv.id = this.divid + \"-startWrapper\";\n this.timerContainer.id = this.divid + \"-output\";\n this.wrapperDiv.appendChild(this.timerContainer);\n this.showTime();\n }\n\n renderControlButtons() {\n this.controlDiv = document.createElement(\"div\");\n $(this.controlDiv).attr({\n id: \"controls\",\n style: \"text-align: center\",\n });\n this.startBtn = document.createElement(\"button\");\n this.pauseBtn = document.createElement(\"button\");\n $(this.startBtn).attr({\n class: \"btn btn-success\",\n id: \"start\",\n tabindex: \"0\",\n role: \"button\",\n });\n this.startBtn.textContent = \"Start\";\n this.startBtn.addEventListener(\n \"click\",\n async function () {\n $(this.finishButton).hide(); // hide the finish button for now\n $(this.flagButton).show();\n let mess = document.createElement(\"p\");\n mess.innerHTML =\n \"Warning: You will not be able to continue the exam if you close this tab, close the window, or navigate away from this page! Make sure you click the Finish Exam button when you are done to submit your work!\";\n this.controlDiv.appendChild(mess);\n mess.classList.add(\"examwarning\");\n await this.renderTimedQuestion();\n this.startAssessment();\n }.bind(this),\n false\n );\n $(this.pauseBtn).attr({\n class: \"btn btn-default\",\n id: \"pause\",\n disabled: \"true\",\n tabindex: \"0\",\n role: \"button\",\n });\n this.pauseBtn.textContent = \"Pause\";\n this.pauseBtn.addEventListener(\n \"click\",\n function () {\n this.pauseAssessment();\n }.bind(this),\n false\n );\n if (!this.taken) {\n this.controlDiv.appendChild(this.startBtn);\n }\n if (!this.nopause) {\n this.controlDiv.appendChild(this.pauseBtn);\n }\n this.containerDiv.appendChild(this.wrapperDiv);\n this.containerDiv.appendChild(this.controlDiv);\n }\n\n renderNavControls() {\n // making \"Prev\" button\n this.pagNavList = document.createElement(\"ul\");\n $(this.pagNavList).addClass(\"pagination\");\n this.leftContainer = document.createElement(\"li\");\n this.leftNavButton = document.createElement(\"button\");\n this.leftNavButton.innerHTML = \"‹ Prev\";\n $(this.leftNavButton).attr(\"aria-label\", \"Previous\");\n $(this.leftNavButton).attr(\"tabindex\", \"0\");\n $(this.leftNavButton).attr(\"role\", \"button\");\n $(this.rightNavButton).attr(\"id\", \"prev\");\n $(this.leftNavButton).css(\"cursor\", \"pointer\");\n this.leftContainer.appendChild(this.leftNavButton);\n this.pagNavList.appendChild(this.leftContainer);\n // making \"Flag Question\" button\n this.flaggingPlace = document.createElement(\"ul\");\n $(this.flaggingPlace).addClass(\"pagination\");\n this.flagContainer = document.createElement(\"li\");\n this.flagButton = document.createElement(\"button\");\n $(this.flagButton).addClass(\"flagBtn\");\n this.flagButton.innerHTML = \"Flag Question\"; // name on button\n $(this.flagButton).attr(\"aria-labelledby\", \"Flag\");\n $(this.flagButton).attr(\"tabindex\", \"5\");\n $(this.flagButton).attr(\"role\", \"button\");\n $(this.flagButton).attr(\"id\", \"flag\");\n $(this.flagButton).css(\"cursor\", \"pointer\");\n this.flagContainer.appendChild(this.flagButton); // adding button to container\n this.flaggingPlace.appendChild(this.flagContainer); // adding container to flaggingPlace\n // making \"Next\" button\n this.rightContainer = document.createElement(\"li\");\n this.rightNavButton = document.createElement(\"button\");\n $(this.rightNavButton).attr(\"aria-label\", \"Next\");\n $(this.rightNavButton).attr(\"tabindex\", \"0\");\n $(this.rightNavButton).attr(\"role\", \"button\");\n $(this.rightNavButton).attr(\"id\", \"next\");\n this.rightNavButton.innerHTML = \"Next ›\";\n $(this.rightNavButton).css(\"cursor\", \"pointer\");\n this.rightContainer.appendChild(this.rightNavButton);\n this.pagNavList.appendChild(this.rightContainer);\n this.ensureButtonSafety();\n this.navDiv.appendChild(this.pagNavList);\n this.flagDiv.appendChild(this.flaggingPlace); // adds flaggingPlace to the flagDiv\n this.break = document.createElement(\"br\");\n this.navDiv.appendChild(this.break);\n // render the question number jump buttons\n this.qNumList = document.createElement(\"ul\");\n $(this.qNumList).attr(\"id\", \"pageNums\");\n this.qNumWrapperList = document.createElement(\"ul\");\n $(this.qNumWrapperList).addClass(\"pagination\");\n var tmpLi, tmpA;\n for (var i = 0; i < this.renderedQuestionArray.length; i++) {\n tmpLi = document.createElement(\"li\");\n tmpA = document.createElement(\"a\");\n tmpA.innerHTML = i + 1;\n $(tmpA).css(\"cursor\", \"pointer\");\n if (i === 0) {\n $(tmpLi).addClass(\"active\");\n }\n tmpLi.appendChild(tmpA);\n this.qNumWrapperList.appendChild(tmpLi);\n }\n this.qNumList.appendChild(this.qNumWrapperList);\n this.navDiv.appendChild(this.qNumList);\n this.navBtnListeners();\n this.flagBtnListener(); // listens for click on flag button\n $(this.flagButton).hide();\n }\n\n // when moving off of a question in an active exam:\n // 1. show that the question has been seen, or mark it broken if it is in error.\n // 2. check and log the current answer\n async navigateAway() {\n if (\n this.renderedQuestionArray[this.currentQuestionIndex].state ==\n \"broken_exam\"\n ) {\n $(\n \"ul#pageNums > ul > li:eq(\" + this.currentQuestionIndex + \")\"\n ).addClass(\"broken\");\n }\n if (\n this.renderedQuestionArray[this.currentQuestionIndex].state ==\n \"exam_ended\"\n ) {\n $(\n \"ul#pageNums > ul > li:eq(\" + this.currentQuestionIndex + \")\"\n ).addClass(\"toolate\");\n }\n if (\n this.renderedQuestionArray[this.currentQuestionIndex].question\n .isAnswered\n ) {\n $(\n \"ul#pageNums > ul > li:eq(\" + this.currentQuestionIndex + \")\"\n ).addClass(\"answered\");\n await this.renderedQuestionArray[\n this.currentQuestionIndex\n ].question.checkCurrentAnswer();\n if (!this.done) {\n await this.renderedQuestionArray[\n this.currentQuestionIndex\n ].question.logCurrentAnswer();\n }\n }\n }\n async handleNextPrev(event) {\n if (!this.taken) {\n await this.navigateAway();\n }\n var target = $(event.target).text();\n if (target.match(/Next/)) {\n // checks given text to match \"Next\"\n if ($(this.rightContainer).hasClass(\"disabled\")) {\n return;\n }\n this.currentQuestionIndex++;\n } else if (target.match(/Prev/)) {\n // checks given text to match \"Prev\"\n if ($(this.leftContainer).hasClass(\"disabled\")) {\n return;\n }\n this.currentQuestionIndex--;\n }\n await this.renderTimedQuestion();\n this.ensureButtonSafety();\n for (var i = 0; i < this.qNumList.childNodes.length; i++) {\n for (\n var j = 0;\n j < this.qNumList.childNodes[i].childNodes.length;\n j++\n ) {\n $(this.qNumList.childNodes[i].childNodes[j]).removeClass(\n \"active\"\n );\n }\n }\n $(\n \"ul#pageNums > ul > li:eq(\" + this.currentQuestionIndex + \")\"\n ).addClass(\"active\");\n if (\n $(\n \"ul#pageNums > ul > li:eq(\" + this.currentQuestionIndex + \")\"\n ).hasClass(\"flagcolor\")\n ) {\n // checking for class\n this.flagButton.innerHTML = \"Unflag Question\"; // changes text on button\n } else {\n this.flagButton.innerHTML = \"Flag Question\"; // changes text on button\n }\n }\n\n async handleFlag(event) {\n // called when flag button is clicked\n var target = $(event.target).text();\n if (target.match(/Flag Question/)) {\n $(\n \"ul#pageNums > ul > li:eq(\" + this.currentQuestionIndex + \")\"\n ).addClass(\"flagcolor\"); // class will change color of question block\n this.flagButton.innerHTML = \"Unflag Question\";\n } else {\n $(\n \"ul#pageNums > ul > li:eq(\" + this.currentQuestionIndex + \")\"\n ).removeClass(\"flagcolor\"); // will restore current color of question block\n this.flagButton.innerHTML = \"Flag Question\"; // also sets name back\n }\n }\n\n async handleNumberedNav(event) {\n if (!this.taken) {\n await this.navigateAway();\n }\n for (var i = 0; i < this.qNumList.childNodes.length; i++) {\n for (\n var j = 0;\n j < this.qNumList.childNodes[i].childNodes.length;\n j++\n ) {\n $(this.qNumList.childNodes[i].childNodes[j]).removeClass(\n \"active\"\n );\n }\n }\n\n var target = $(event.target).text();\n let oldIndex = this.currentQuestionIndex;\n this.currentQuestionIndex = parseInt(target) - 1;\n if (this.currentQuestionIndex > this.renderedQuestionArray.length) {\n console.log(`Error: bad index for ${target}`);\n this.currentQuestionIndex = oldIndex;\n }\n $(\n \"ul#pageNums > ul > li:eq(\" + this.currentQuestionIndex + \")\"\n ).addClass(\"active\");\n if (\n $(\n \"ul#pageNums > ul > li:eq(\" + this.currentQuestionIndex + \")\" // checking for flagcolor class\n ).hasClass(\"flagcolor\")\n ) {\n this.flagButton.innerHTML = \"Unflag Question\";\n } else {\n this.flagButton.innerHTML = \"Flag Question\";\n }\n await this.renderTimedQuestion();\n this.ensureButtonSafety();\n }\n\n // set up events for navigation\n navBtnListeners() {\n // Next and Prev Listener\n this.pagNavList.addEventListener(\n \"click\",\n this.handleNextPrev.bind(this),\n false\n );\n\n // Numbered Listener\n this.qNumList.addEventListener(\n \"click\",\n this.handleNumberedNav.bind(this),\n false\n );\n }\n\n // set up event for flag\n flagBtnListener() {\n this.flaggingPlace.addEventListener(\n \"click\",\n this.handleFlag.bind(this), // calls this to take action\n false\n );\n }\n\n renderSubmitButton() {\n this.buttonContainer = document.createElement(\"div\");\n $(this.buttonContainer).attr({\n style: \"text-align:center\",\n });\n this.finishButton = document.createElement(\"button\");\n $(this.finishButton).attr({\n id: \"finish\",\n class: \"btn btn-primary\",\n });\n this.finishButton.textContent = \"Finish Exam\";\n this.finishButton.addEventListener(\n \"click\",\n async function () {\n let skipped =\n this.renderedQuestionArray.filter((x) => !x.question.isAnswered).length;\n let skipstr = skipped > 0 ? `You have skipped ${skipped} question(s).` : \"\";\n if (\n window.confirm(\n `${skipstr} Clicking OK means you are ready to submit your answers and are finished with this assessment.`\n )\n ) {\n await this.finishAssessment();\n $(this.flagButton).hide();\n }\n }.bind(this),\n false\n );\n this.controlDiv.appendChild(this.finishButton);\n $(this.finishButton).hide();\n this.timedDiv.appendChild(this.buttonContainer);\n }\n ensureButtonSafety() {\n if (this.currentQuestionIndex === 0) {\n if (this.renderedQuestionArray.length != 1) {\n $(this.rightContainer).removeClass(\"disabled\");\n }\n $(this.leftContainer).addClass(\"disabled\");\n }\n if (\n this.currentQuestionIndex >=\n this.renderedQuestionArray.length - 1\n ) {\n if (this.renderedQuestionArray.length != 1) {\n $(this.leftContainer).removeClass(\"disabled\");\n }\n $(this.rightContainer).addClass(\"disabled\");\n }\n if (\n this.currentQuestionIndex > 0 &&\n this.currentQuestionIndex < this.renderedQuestionArray.length - 1\n ) {\n $(this.rightContainer).removeClass(\"disabled\");\n $(this.leftContainer).removeClass(\"disabled\");\n }\n }\n renderFeedbackContainer() {\n this.scoreDiv = document.createElement(\"P\");\n if (this.taken) {\n this.scoreDiv.innerHTML = \"

You have already taken this exam

\";\n this.scoreDiv.style.display = \"block\";\n } else {\n this.scoreDiv.id = this.divid + \"results\";\n this.scoreDiv.style.display = \"none\";\n }\n this.containerDiv.appendChild(this.scoreDiv);\n }\n\n createRenderedQuestionArray() {\n // this finds all the assess questions in this timed assessment\n // We need to make a list of all the questions up front so we can set up navigation\n // but we do not want to render the questions until the student has navigated\n // Also adds them to this.renderedQuestionArray\n\n // todo: This needs to be updated to account for the runestone div wrapper.\n\n // To accommodate the selectquestion type -- which is async! we need to wrap\n // all of this in a promise, so that we don't continue to render the timed\n // exam until all of the questions have been realized.\n var opts;\n for (var i = 0; i < this.newChildren.length; i++) {\n var tmpChild = this.newChildren[i];\n opts = {\n state: \"prepared\",\n orig: tmpChild,\n question: {},\n useRunestoneServices: eBookConfig.useRunestoneServices,\n timed: true,\n assessmentTaken: this.taken,\n timedWrapper: this.divid,\n initAttempts: 0,\n };\n if ($(tmpChild).children(\"[data-component]\").length > 0) {\n tmpChild = $(tmpChild).children(\"[data-component]\")[0];\n opts.orig = tmpChild;\n }\n if ($(tmpChild).is(\"[data-component]\")) {\n this.renderedQuestionArray.push(opts);\n }\n }\n }\n\n randomizeRQA() {\n var currentIndex = this.renderedQuestionArray.length,\n temporaryValue,\n randomIndex;\n // While there remain elements to shuffle...\n while (currentIndex !== 0) {\n // Pick a remaining element...\n randomIndex = Math.floor(Math.random() * currentIndex);\n currentIndex -= 1;\n // And swap it with the current element.\n temporaryValue = this.renderedQuestionArray[currentIndex];\n this.renderedQuestionArray[currentIndex] =\n this.renderedQuestionArray[randomIndex];\n this.renderedQuestionArray[randomIndex] = temporaryValue;\n }\n }\n\n async renderTimedQuestion() {\n if (this.currentQuestionIndex >= this.renderedQuestionArray.length) {\n // sometimes the user clicks in the event area for the qNumList\n // But misses a number in that case the text is the concatenation\n // of all the numbers in the list!\n return;\n }\n // check the renderedQuestionArray to see if it has been rendered.\n let opts = this.renderedQuestionArray[this.currentQuestionIndex];\n let currentQuestion;\n if (\n opts.state === \"prepared\" ||\n opts.state === \"forreview\" ||\n (opts.state === \"broken_exam\" && opts.initAttempts < 3)\n ) {\n let tmpChild = opts.orig;\n if ($(tmpChild).is(\"[data-component=selectquestion]\")) {\n if (this.done && opts.state == \"prepared\") {\n this.renderedQuestionArray[\n this.currentQuestionIndex\n ].state = \"exam_ended\";\n } else {\n // SelectOne is async and will replace itself in this array with\n // the actual selected question\n opts.rqa = this.renderedQuestionArray;\n let newq = new SelectOne(opts);\n this.renderedQuestionArray[this.currentQuestionIndex] = {\n question: newq,\n };\n try {\n await newq.initialize();\n if (opts.state == \"broken_exam\") {\n // remove the broken class from this question if we get here.\n $(\n `ul#pageNums > ul > li:eq(${this.currentQuestionIndex})`\n ).removeClass(\"broken\");\n }\n } catch (e) {\n opts.state = \"broken_exam\";\n this.renderedQuestionArray[this.currentQuestionIndex] =\n opts;\n console.log(\n `Error initializing question: Details ${e}`\n );\n }\n }\n } else if ($(tmpChild).is(\"[data-component]\")) {\n let componentKind = $(tmpChild).data(\"component\");\n this.renderedQuestionArray[this.currentQuestionIndex] = {\n question: window.component_factory[componentKind](opts),\n state: opts.state,\n };\n }\n } else if (opts.state === \"broken_exam\") {\n return;\n }\n\n currentQuestion =\n this.renderedQuestionArray[this.currentQuestionIndex].question;\n if (opts.state === \"forreview\") {\n await currentQuestion.component_ready_promise;\n await currentQuestion.checkCurrentAnswer();\n currentQuestion.renderFeedback();\n currentQuestion.disableInteraction();\n }\n\n if (!this.visited.includes(this.currentQuestionIndex)) {\n this.visited.push(this.currentQuestionIndex);\n if (\n this.visited.length === this.renderedQuestionArray.length &&\n !this.done\n ) {\n $(this.finishButton).show();\n }\n }\n\n if (currentQuestion.containerDiv) {\n if (\n currentQuestion.containerDiv.classList.contains(\"runestone\") ==\n false\n ) {\n currentQuestion.containerDiv.classList.add(\"runestone\");\n }\n $(this.switchDiv).replaceWith(currentQuestion.containerDiv);\n this.switchDiv = currentQuestion.containerDiv;\n }\n\n // If the timed component has listeners, those might need to be reinitialized\n // This flag will only be set in the elements that need it--it will be undefined in the others and thus evaluate to false\n if (currentQuestion.needsReinitialization) {\n currentQuestion.reinitializeListeners(this.taken);\n }\n }\n\n /*=================================\n === Timer and control Functions ===\n =================================*/\n handlePrevAssessment() {\n $(this.startBtn).hide();\n $(this.pauseBtn).attr(\"disabled\", true);\n $(this.finishButton).attr(\"disabled\", true);\n this.running = 0;\n this.done = 1;\n // showFeedback sand showResults should both be true before we show the\n // questions and their state of correctness.\n if (this.showResults && this.showFeedback) {\n $(this.timedDiv).show();\n this.restoreAnsweredQuestions(); // do not log these results\n } else {\n $(this.pauseBtn).hide();\n $(this.timerContainer).hide();\n }\n }\n startAssessment() {\n if (!this.taken) {\n $(\"#relations-next\").hide(); // hide the next page button for now\n $(\"#relations-prev\").hide(); // hide the previous button for now\n $(this.startBtn).hide();\n $(this.pauseBtn).attr(\"disabled\", false);\n if (this.running === 0 && this.paused === 0) {\n this.running = 1;\n this.lastTime = Date.now();\n $(this.timedDiv).show();\n this.increment();\n this.logBookEvent({\n event: \"timedExam\",\n act: \"start\",\n div_id: this.divid,\n });\n var timeStamp = new Date();\n var storageObj = {\n answer: [0, 0, this.renderedQuestionArray.length, 0],\n timestamp: timeStamp,\n };\n localStorage.setItem(\n this.localStorageKey(),\n JSON.stringify(storageObj)\n );\n }\n $(window).on(\n \"beforeunload\",\n function (event) {\n // this actual value gets ignored by newer browsers\n if (this.done) {\n return;\n }\n event.preventDefault();\n event.returnValue =\n \"Are you sure you want to leave? Your work will be lost! And you will need your instructor to reset the exam!\";\n return \"Are you sure you want to leave? Your work will be lost!\";\n }.bind(this)\n );\n window.addEventListener(\n \"pagehide\",\n async function (event) {\n if (!this.done) {\n await this.finishAssessment();\n console.log(\"Exam exited by leaving page\");\n }\n }.bind(this)\n );\n } else {\n this.handlePrevAssessment();\n }\n }\n pauseAssessment() {\n if (this.done === 0) {\n if (this.running === 1) {\n this.logBookEvent({\n event: \"timedExam\",\n act: \"pause\",\n div_id: this.divid,\n });\n this.running = 0;\n this.paused = 1;\n this.pauseBtn.innerHTML = \"Resume\";\n $(this.timedDiv).hide();\n } else {\n this.logBookEvent({\n event: \"timedExam\",\n act: \"resume\",\n div_id: this.divid,\n });\n this.running = 1;\n this.paused = 0;\n this.increment();\n this.pauseBtn.innerHTML = \"Pause\";\n $(this.timedDiv).show();\n }\n }\n }\n\n showTime() {\n if (this.showTimer) {\n var mins = Math.floor(this.timeLimit / 60);\n var secs = Math.floor(this.timeLimit) % 60;\n var minsString = mins;\n var secsString = secs;\n if (mins < 10) {\n minsString = \"0\" + mins;\n }\n if (secs < 10) {\n secsString = \"0\" + secs;\n }\n var beginning = \"Time Remaining \";\n if (!this.limitedTime) {\n beginning = \"Time Taken \";\n }\n var timeString = beginning + minsString + \":\" + secsString;\n if (this.done || this.taken) {\n var minutes = Math.floor(this.timeTaken / 60);\n var seconds = Math.floor(this.timeTaken % 60);\n if (minutes < 10) {\n minutes = \"0\" + minutes;\n }\n if (seconds < 10) {\n seconds = \"0\" + seconds;\n }\n timeString = \"Time taken: \" + minutes + \":\" + seconds;\n }\n this.timerContainer.innerHTML = timeString;\n var timeTips = document.getElementsByClassName(\"timeTip\");\n for (var i = 0; i <= timeTips.length - 1; i++) {\n timeTips[i].title = timeString;\n }\n } else {\n $(this.timerContainer).hide();\n }\n }\n\n increment() {\n // if running (not paused) and not taken\n if (this.running === 1 && !this.taken) {\n setTimeout(\n function () {\n // When a browser loses focus, setTimeout may not be called on the\n // schedule expected. Browsers are free to save power by lengthening\n // the interval to some longer time. So we cannot just subtract 1\n // from the timeLimit we need to measure the elapsed time from the last\n // call to the current call and subtract that number of seconds.\n let currentTime = Date.now();\n if (this.limitedTime) {\n // If there's a time limit, count down to 0\n this.timeLimit =\n this.timeLimit -\n Math.floor((currentTime - this.lastTime) / 1000);\n } else {\n // Else count up to keep track of how long it took to complete\n this.timeLimit =\n this.timeLimit +\n Math.floor((currentTime - this.lastTime) / 1000);\n }\n this.lastTime = currentTime;\n localStorage.setItem(\n eBookConfig.email + \":\" + this.divid + \"-time\",\n this.timeLimit\n );\n this.showTime();\n if (this.timeLimit > 0) {\n this.increment();\n // ran out of time\n } else {\n $(this.startBtn).attr({\n disabled: \"true\",\n });\n $(this.finishButton).attr({\n disabled: \"true\",\n });\n this.running = 0;\n this.done = 1;\n if (!this.taken) {\n this.taken = true;\n // embed the message in the page -- an alert actually prevents\n // the answers from being submitted and if a student closes their\n // laptop then the answers will not be submitted ever! Even when they\n // reopen the laptop their session cookie is likely invalid.\n let mess = document.createElement(\"h1\");\n mess.innerHTML =\n \"Sorry but you ran out of time. Your answers are being submitted\";\n this.controlDiv.appendChild(mess);\n this.finishAssessment();\n }\n }\n }.bind(this),\n 1000\n );\n }\n }\n\n styleExamElements() {\n // Checks if this exam has been taken before\n $(this.timerContainer).css({\n width: \"50%\",\n margin: \"0 auto\",\n \"background-color\": \"#DFF0D8\",\n \"text-align\": \"center\",\n border: \"2px solid #DFF0D8\",\n \"border-radius\": \"25px\",\n });\n $(this.scoreDiv).css({\n width: \"50%\",\n margin: \"0 auto\",\n \"background-color\": \"#DFF0D8\",\n \"text-align\": \"center\",\n border: \"2px solid #DFF0D8\",\n \"border-radius\": \"25px\",\n });\n $(\".tooltipTime\").css({\n margin: \"0\",\n padding: \"0\",\n \"background-color\": \"black\",\n color: \"white\",\n });\n }\n\n async finishAssessment() {\n $(\"#relations-next\").show(); // show the next page button for now\n $(\"#relations-prev\").show(); // show the previous button for now\n if (!this.showFeedback) {\n // bje - changed from showResults\n $(this.timedDiv).hide();\n $(this.pauseBtn).hide();\n $(this.timerContainer).hide();\n }\n this.findTimeTaken();\n this.running = 0;\n this.done = 1;\n this.taken = 1;\n await this.finalizeProblems();\n this.checkScore();\n this.displayScore();\n this.storeScore();\n this.logScore();\n $(this.pauseBtn).attr(\"disabled\", true);\n this.finishButton.disabled = true;\n $(window).off(\"beforeunload\");\n // turn off the pagehide listener\n let assignment_id = this.divid;\n setTimeout(function () {\n jQuery.ajax({\n url: eBookConfig.app + \"/assignments/student_autograde\",\n type: \"POST\",\n dataType: \"JSON\",\n data: {\n assignment_id: assignment_id,\n is_timed: true,\n },\n success: function (retdata) {\n if (retdata.success == false) {\n console.log(retdata.message);\n } else {\n console.log(\"Autograder completed\");\n }\n },\n });\n }, 2000);\n }\n\n // finalizeProblems\n // ----------------\n async finalizeProblems() {\n // Because we have submitted each question as we navigate we only need to\n // send the final version of the question the student is on when they press the\n // finish exam button.\n\n var currentQuestion =\n this.renderedQuestionArray[this.currentQuestionIndex].question;\n await currentQuestion.checkCurrentAnswer();\n await currentQuestion.logCurrentAnswer();\n currentQuestion.renderFeedback();\n currentQuestion.disableInteraction();\n\n for (var i = 0; i < this.renderedQuestionArray.length; i++) {\n let currentQuestion = this.renderedQuestionArray[i];\n // set the state to forreview so we know that feedback may be appropriate\n if (currentQuestion.state !== \"broken_exam\") {\n currentQuestion.state = \"forreview\";\n currentQuestion.question.disableInteraction();\n }\n }\n\n if (!this.showFeedback) {\n this.hideTimedFeedback();\n }\n }\n\n // restoreAnsweredQuestions\n // ------------------------\n restoreAnsweredQuestions() {\n for (var i = 0; i < this.renderedQuestionArray.length; i++) {\n var currentQuestion = this.renderedQuestionArray[i];\n if (currentQuestion.state === \"prepared\") {\n currentQuestion.state = \"forreview\";\n }\n }\n }\n\n // hideTimedFeedback\n // -----------------\n hideTimedFeedback() {\n for (var i = 0; i < this.renderedQuestionArray.length; i++) {\n var currentQuestion = this.renderedQuestionArray[i].question;\n currentQuestion.hideFeedback();\n }\n }\n\n // checkScore\n // ----------\n // This is a simple all or nothing score of one point per question for\n // that includes our best guess if a question was skipped.\n checkScore() {\n this.correctStr = \"\";\n this.skippedStr = \"\";\n this.incorrectStr = \"\";\n // Gets the score of each problem\n for (var i = 0; i < this.renderedQuestionArray.length; i++) {\n var correct =\n this.renderedQuestionArray[i].question.checkCorrectTimed();\n if (correct == \"T\") {\n this.score++;\n this.correctStr = this.correctStr + (i + 1) + \", \";\n } else if (correct == \"F\") {\n this.incorrect++;\n this.incorrectStr = this.incorrectStr + (i + 1) + \", \";\n } else if (correct === null || correct === \"I\") {\n this.skipped++;\n this.skippedStr = this.skippedStr + (i + 1) + \", \";\n } else {\n // ignored question; just do nothing\n }\n }\n // remove extra comma and space at end if any\n if (this.correctStr.length > 0)\n this.correctStr = this.correctStr.substring(\n 0,\n this.correctStr.length - 2\n );\n else this.correctStr = \"None\";\n if (this.skippedStr.length > 0)\n this.skippedStr = this.skippedStr.substring(\n 0,\n this.skippedStr.length - 2\n );\n else this.skippedStr = \"None\";\n if (this.incorrectStr.length > 0)\n this.incorrectStr = this.incorrectStr.substring(\n 0,\n this.incorrectStr.length - 2\n );\n else this.incorrectStr = \"None\";\n }\n findTimeTaken() {\n if (this.limitedTime) {\n this.timeTaken = this.startingTime - this.timeLimit;\n } else {\n this.timeTaken = this.timeLimit;\n }\n }\n storeScore() {\n var storage_arr = [];\n storage_arr.push(\n this.score,\n this.correctStr,\n this.incorrect,\n this.incorrectStr,\n this.skipped,\n this.skippedStr,\n this.timeTaken\n );\n var timeStamp = new Date();\n var storageObj = JSON.stringify({\n answer: storage_arr,\n timestamp: timeStamp,\n });\n localStorage.setItem(this.localStorageKey(), storageObj);\n }\n // _`timed exam endpoint parameters`\n //----------------------------------\n logScore() {\n this.logBookEvent({\n event: \"timedExam\",\n act: \"finish\",\n div_id: this.divid,\n correct: this.score,\n incorrect: this.incorrect,\n skipped: this.skipped,\n time_taken: this.timeTaken,\n });\n }\n shouldUseServer(data) {\n // We override the RunestoneBase version because there is no \"correct\" attribute, and there are 2 possible localStorage schemas\n // --we also want to default to local storage because it contains more information specifically which questions are correct, incorrect, and skipped.\n var storageDate;\n if (localStorage.length === 0) return true;\n var storageObj = localStorage.getItem(this.localStorageKey());\n if (storageObj === null) return true;\n try {\n var storedData = JSON.parse(storageObj).answer;\n if (storedData.length == 4) {\n if (\n data.correct == storedData[0] &&\n data.incorrect == storedData[1] &&\n data.skipped == storedData[2] &&\n data.timeTaken == storedData[3]\n )\n return true;\n } else if (storedData.length == 7) {\n if (\n data.correct == storedData[0] &&\n data.incorrect == storedData[2] &&\n data.skipped == storedData[4] &&\n data.timeTaken == storedData[6]\n ) {\n return false; // In this case, because local storage has more info, we want to use that if it's consistent\n }\n }\n storageDate = new Date(JSON.parse(storageObj[1]).timestamp);\n } catch (err) {\n // error while parsing; likely due to bad value stored in storage\n console.log(err.message);\n localStorage.removeItem(this.localStorageKey());\n return true;\n }\n var serverDate = new Date(data.timestamp);\n if (serverDate < storageDate) {\n this.logScore();\n return false;\n }\n return true;\n }\n\n checkLocalStorage() {\n var len = localStorage.length;\n if (len > 0) {\n if (localStorage.getItem(this.localStorageKey()) !== null) {\n this.taken = 1;\n this.restoreAnswers(\"\");\n } else {\n this.taken = 0;\n }\n } else {\n this.taken = 0;\n }\n }\n async restoreAnswers(data) {\n this.taken = 1;\n var tmpArr;\n if (data === \"\") {\n let error = false;\n let storageObj;\n try {\n storageObj = JSON.parse(\n localStorage.getItem(this.localStorageKey())\n );\n tmpArr = storageObj.answer;\n } catch (err) {\n // error while parsing; likely due to bad value stored in storage\n console.log(`Error parsing stored Timed data for ${this.divid}: ${err.message}`);\n error = true;\n }\n if (error || storageObj.timestamp < eBookConfig.termStartDate) {\n localStorage.removeItem(this.localStorageKey());\n this.taken = 0;\n return;\n }\n } else {\n // Parse results from the database\n tmpArr = [\n parseInt(data.correct),\n parseInt(data.incorrect),\n parseInt(data.skipped),\n parseInt(data.time_taken),\n data.reset,\n ];\n this.setLocalStorage(tmpArr);\n }\n if (tmpArr.length == 1) {\n // Exam was previously reset\n this.reset = true;\n this.taken = 0;\n return;\n }\n if (tmpArr.length == 4) {\n // Accidental Reload OR Database Entry\n this.score = tmpArr[0];\n this.incorrect = tmpArr[1];\n this.skipped = tmpArr[2];\n this.timeTaken = tmpArr[3];\n } else if (tmpArr.length == 5) {\n this.score = tmpArr[0];\n this.incorrect = tmpArr[1];\n this.skipped = tmpArr[2];\n this.timeTaken = tmpArr[3];\n } else if (tmpArr.length == 7) {\n // Loaded Completed Exam\n this.score = tmpArr[0];\n this.correctStr = tmpArr[1];\n this.incorrect = tmpArr[2];\n this.incorrectStr = tmpArr[3];\n this.skipped = tmpArr[4];\n this.skippedStr = tmpArr[5];\n this.timeTaken = tmpArr[6];\n } else {\n // Set localStorage in case of \"accidental\" reload\n this.score = 0;\n this.incorrect = 0;\n this.skipped = this.renderedQuestionArray.length;\n this.timeTaken = 0;\n }\n if (this.taken) {\n if (this.skipped === this.renderedQuestionArray.length) {\n this.showFeedback = false;\n }\n this.handlePrevAssessment();\n }\n await this.renderTimedQuestion();\n this.displayScore();\n this.showTime();\n }\n setLocalStorage(parsedData) {\n var timeStamp = new Date();\n var storageObj = {\n answer: parsedData,\n timestamp: timeStamp,\n };\n localStorage.setItem(\n this.localStorageKey(),\n JSON.stringify(storageObj)\n );\n }\n displayScore() {\n if (this.showResults) {\n var scoreString = \"\";\n var numQuestions;\n var percentCorrect;\n // if we have some information\n if (\n this.correctStr.length > 0 ||\n this.incorrectStr.length > 0 ||\n this.skippedStr.length > 0\n ) {\n scoreString = `Num Correct: ${this.score}. Questions: ${this.correctStr}
Num Wrong: ${this.incorrect}. Questions: ${this.incorrectStr}
Num Skipped: ${this.skipped}. Questions: ${this.skippedStr}
`;\n numQuestions = this.score + this.incorrect + this.skipped;\n percentCorrect = (this.score / numQuestions) * 100;\n scoreString +=\n \"Percent Correct: \" + percentCorrect.toFixed(2) + \"%\";\n $(this.scoreDiv).html(scoreString);\n this.scoreDiv.style.display = \"block\";\n } else {\n scoreString = `Num Correct: ${this.score}
Num Wrong: ${this.incorrect}
Num Skipped: ${this.skipped}
`;\n numQuestions = this.score + this.incorrect + this.skipped;\n percentCorrect = (this.score / numQuestions) * 100;\n scoreString +=\n \"Percent Correct: \" + percentCorrect.toFixed(2) + \"%\";\n $(this.scoreDiv).html(scoreString);\n this.scoreDiv.style.display = \"block\";\n }\n this.highlightNumberedList();\n } else {\n $(this.scoreDiv).html(\n \"Thank you for taking the exam. 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+

Math 1044 Notes

+

Andy Eisenberg

+
+
+
+

+Section B.1 \(\chi^2\) Critical Values +

+
Table B.1.1. \(\chi^2\) Critical Values
🔗
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Degrees of FreedomCritical value for \(p = 0.05\) +
\(1\)\(3.841\)
\(2\)\(5.991\)
\(3\)\(7.815\)
\(4\)\(9.488\)
\(5\)\(11.070\)
\(6\)\(12.592\)
\(7\)\(14.067\)
\(8\)\(15.507\)
\(9\)\(16.919\)
\(10\)\(18.307\)
🔗
+
+PrevTopNext +
+
+
+ +
+ + diff --git a/app-Phi-table.html b/app-Phi-table.html index 13b16c2..bb5e824 100755 --- a/app-Phi-table.html +++ b/app-Phi-table.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
A \(\Phi(z)\) Table
-
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/backmatter-2.html b/backmatter-2.html index e2f3e83..1d4c1dc 100755 --- a/backmatter-2.html +++ b/backmatter-2.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/backmatter-3.html b/backmatter-3.html index 344a46f..f5ee3c4 100755 --- a/backmatter-3.html +++ b/backmatter-3.html @@ -14,7 +14,7 @@ -Colophon +\chi^2 Critical Values Table @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -135,7 +135,7 @@ eBookConfig.enable_chatcodes = false; -PrevUpNext +PrevUpNext -

    -Colophon Colophon +

    +Appendix B \(\chi^2\) Critical Values Table

    -
    This book was authored in PreTeXt.
    🔗
    -
    -
    🔗
    +
    🔗

    -PrevTopNext +PrevTopNext
    diff --git a/backmatter-4.html b/backmatter-4.html new file mode 100755 index 0000000..20d2434 --- /dev/null +++ b/backmatter-4.html @@ -0,0 +1,327 @@ + + + + + + + + + + + + + + + + +Colophon + + + + + + + + + + + + + + + + + + + + +Skip to main content
    +

    Math 1044 Notes

    +

    Andy Eisenberg

    +
    +
    +
    +

    +Colophon Colophon +

    +
    This book was authored in PreTeXt.
    🔗
    +
    +
    🔗
    +
    +PrevTopNext +
    +
    +
    + +
    + + diff --git a/backmatter.html b/backmatter.html index f7f47cd..d6d3c73 100755 --- a/backmatter.html +++ b/backmatter.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,13 +302,18 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • 🔗
    PrevTopNext diff --git a/ch-Confidence-Intervals.html b/ch-Confidence-Intervals.html index 7cee3b6..224ebe1 100755 --- a/ch-Confidence-Intervals.html +++ b/ch-Confidence-Intervals.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/ch-Expected-Value.html b/ch-Expected-Value.html index 9e5bcf9..bb98218 100755 --- a/ch-Expected-Value.html +++ b/ch-Expected-Value.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/ch-Hypothesis-Testing.html b/ch-Hypothesis-Testing.html index 3ae46a2..ea1feaf 100755 --- a/ch-Hypothesis-Testing.html +++ b/ch-Hypothesis-Testing.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/ch-Introduction.html b/ch-Introduction.html index 210a58f..cffe6fa 100755 --- a/ch-Introduction.html +++ b/ch-Introduction.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/ch-Linear-Regression.html b/ch-Linear-Regression.html index 7aaf43c..320a47b 100755 --- a/ch-Linear-Regression.html +++ b/ch-Linear-Regression.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/ch-Probability.html b/ch-Probability.html index 6c1c3e2..dbcac29 100755 --- a/ch-Probability.html +++ b/ch-Probability.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/ch-Random-Variables.html b/ch-Random-Variables.html index efdf975..277fe3b 100755 --- a/ch-Random-Variables.html +++ b/ch-Random-Variables.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/front-colophon.html b/front-colophon.html index d4eb540..26a5ba4 100755 --- a/front-colophon.html +++ b/front-colophon.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/frontmatter.html b/frontmatter.html index 53d12f1..94c04fa 100755 --- a/frontmatter.html +++ b/frontmatter.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • @@ -311,7 +315,7 @@ eBookConfig.enable_chatcodes = false;
    Andy Eisenberg
    Mathematics Department
    Temple University
    -
    March 19, 2026
    +
    April 2, 2026
    🔗
    PrevTopNext diff --git a/index.html b/index.html index 74e4064..b2cd4a3 100755 --- a/index.html +++ b/index.html @@ -2,7 +2,7 @@ - + diff --git a/knowl/xref/fact-geometric-probability-formula.html b/knowl/xref/fact-geometric-probability-formula.html new file mode 100755 index 0000000..38fdcfd --- /dev/null +++ b/knowl/xref/fact-geometric-probability-formula.html @@ -0,0 +1,34 @@ + + + + + + + + + + + + + + + + + + + + +in-context + + diff --git a/knowl/xref/table-Chi-squared.html b/knowl/xref/table-Chi-squared.html new file mode 100755 index 0000000..349ad2f --- /dev/null +++ b/knowl/xref/table-Chi-squared.html @@ -0,0 +1,69 @@ + + + + + + + + + + + + + + + + + + + + +
    Table B.1.1. \(\chi^2\) Critical Values
    🔗
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    Degrees of FreedomCritical value for \(p = 0.05\) +
    \(1\)\(3.841\)
    \(2\)\(5.991\)
    \(3\)\(7.815\)
    \(4\)\(9.488\)
    \(5\)\(11.070\)
    \(6\)\(12.592\)
    \(7\)\(14.067\)
    \(8\)\(15.507\)
    \(9\)\(16.919\)
    \(10\)\(18.307\)
    in-context + + diff --git a/lunr-pretext-search-index.js b/lunr-pretext-search-index.js index 8b34459..5dd050e 100755 --- a/lunr-pretext-search-index.js +++ b/lunr-pretext-search-index.js @@ -1762,7 +1762,61 @@ var ptx_lunr_docs = [ "type": "Section", "number": "5.4", "title": "\\(\\chi^2\\)<\/span> Test", - "body": " Test Text of section. A store owner wants to determine how much shelf space to allocate to each of the drinks that they sell. They survey their customers about their favorite drinks. Is the data below consistent with the null hypothesis that each type of drink will be equally preferred? drink type water soda tea coffee energy drinks favorite 28 17 15 26 14 A particular drug is administered in 100 independent trials. In each trial, the drug is administered to four people, and we count how many respond to the drug. The table below shows how many trials have each different count of people who respond to the drug. # who respond to drug 0 1 2 3 4 # of trials 3 11 31 34 21 Is the data consistent with a binomial distribution with parameter ? What is the total number of people who have been administered the drug? What is the total number who have responded to it? What is the maximum likelihood estimation for the probability that a person will respond to the drug? Is the data consistent with a binomial distribution with the MLE value of ? " + "body": " Test In our previous hypothesis tests, we've asked about the correct value of some distribution parameter. But we might also be interested in whether a particular type of distribution fits the data in the first place. In this situation, we can try to measure the extent to which the observed data differs from what would be expected under a particular distribution. Suppose are observed data with expected values . The statistic is: The expression directly measures the difference between an observation and its expected value. However, if we simply summed up these differences, then one observation which is higher than its expected value and another that's lower would have differences that cancel out. Squaring the term ensures that any difference contributes positively when summed together. And dividing by ensures that the differences are expressed relative to the size of the expected value. A difference of might sound like a small difference, but it would have a different interpretation if the expected value is than if the expected value is . So the overall number is designed to be a measurement of how much the observed data differs from expectation. It seems like could be higher or lower simply as the result of the number of terms involved in the summation. How much difference is enough to reject the distribution which generated those expected values? It seems that it should depend on that number of terms. If the data collected fall into categories, then we will say that there are degrees of freedom . Suppose our data comes from polling respondents and arranging their responses into categories. Then, if we know how many people fall into categories , we will automatically know how many people fall into the final category, simply because the total number of respondents is already known. For each different number of degrees of freedom, there will be a different critical value of the statistic, above which we'll say that the data differs sufficiently from expectation for us to reject the distribution being tested. A table of critical values is provided in . Suppose people are surveyed about their favorite color among four choices. The results are below. Is this data consistent with the hypothesis that each of the four colors is equally likely to be a favorite? Color Chosen as Favorite Blue Green Purple Red In this case, if each color is equally likely to be a favorite, then we would expect respondents to choose each color. So the statistic is: Since the data fall into four categories, the number of degrees of freedom is . From the table in , the critical value is . Since , our collected data is sufficiently different to reject the hypothesis of equal color preferences. In the previous example, we're testing an extrinsic hypothesis , i.e., a hypothesis made entirely without reference to the data. Knowing that we planned to poll people, we could determine our expected values for this hypothesis before even conducting the survey. However, sometimes we need to use the collected data to estimate the value(s) of one or more parameters of a distribution. In such a situation, we say the hypothesis is intrinsic , and we adjust our calculation of degrees of freedom. Suppose it takes measurements to fully specify the collected data, and suppose there are parameters that are estimated using the data. Then the number of degrees of freedom is Is the data below consistent with a geometric distribution? Number Observation In order to compare this data to a geometric distribution, we would need to know the value of the parameter for the distribution. Based on the collected data, we could provide a maximum likelihood estimate: We can use with the parameter value to generate expected values for our data. For example: so we would expect observations for the number . The rest of the expected values are calculated similarly: Number Observation Expected Now we can calculate the statistic: With categories, it takes measurements to fully specify the data. Then, we used the data itself to estimate the value of one parameter, . So the number of degrees of freedom is , with critical value . Since , our data is not sufficiently different from expected to reject the hypothesis of a geometric distribution. A store owner wants to determine how much shelf space to allocate to each of the drinks that they sell. They survey their customers about their favorite drinks. Is the data below consistent with the null hypothesis that each type of drink will be equally preferred? drink type water soda tea coffee energy drinks favorite 28 17 15 26 14 A particular drug is administered in 100 independent trials. In each trial, the drug is administered to four people, and we count how many respond to the drug. The table below shows how many trials have each different count of people who respond to the drug. # who respond to drug 0 1 2 3 4 # of trials 3 11 31 34 21 Is the data consistent with a binomial distribution with parameter ? What is the total number of people who have been administered the drug? What is the total number who have responded to it? What is the maximum likelihood estimation for the probability that a person will respond to the drug? Is the data consistent with a binomial distribution with the MLE value of ? " +}, +{ + "id": "def-chi-squared", + "level": "2", + "url": "sec-Chi-Squared.html#def-chi-squared", + "type": "Definition", + "number": "5.4.1", + "title": "", + "body": " Suppose are observed data with expected values . The statistic is: " +}, +{ + "id": "def-degrees-of-freedom-1", + "level": "2", + "url": "sec-Chi-Squared.html#def-degrees-of-freedom-1", + "type": "Definition", + "number": "5.4.2", + "title": "", + "body": " If the data collected fall into categories, then we will say that there are degrees of freedom . " +}, +{ + "id": "sec-Chi-Squared-9", + "level": "2", + "url": "sec-Chi-Squared.html#sec-Chi-Squared-9", + "type": "Example", + "number": "5.4.3", + "title": "", + "body": " Suppose people are surveyed about their favorite color among four choices. The results are below. Is this data consistent with the hypothesis that each of the four colors is equally likely to be a favorite? Color Chosen as Favorite Blue Green Purple Red In this case, if each color is equally likely to be a favorite, then we would expect respondents to choose each color. So the statistic is: Since the data fall into four categories, the number of degrees of freedom is . From the table in , the critical value is . Since , our collected data is sufficiently different to reject the hypothesis of equal color preferences. " +}, +{ + "id": "sec-Chi-Squared-10", + "level": "2", + "url": "sec-Chi-Squared.html#sec-Chi-Squared-10", + "type": "Paragraph (with a defined term)", + "number": "", + "title": "", + "body": "extrinsic hypothesis intrinsic " +}, +{ + "id": "def-degrees-of-freedom-2", + "level": "2", + "url": "sec-Chi-Squared.html#def-degrees-of-freedom-2", + "type": "Definition", + "number": "5.4.4", + "title": "", + "body": " Suppose it takes measurements to fully specify the collected data, and suppose there are parameters that are estimated using the data. Then the number of degrees of freedom is " +}, +{ + "id": "sec-Chi-Squared-12", + "level": "2", + "url": "sec-Chi-Squared.html#sec-Chi-Squared-12", + "type": "Example", + "number": "5.4.5", + "title": "", + "body": " Is the data below consistent with a geometric distribution? Number Observation In order to compare this data to a geometric distribution, we would need to know the value of the parameter for the distribution. Based on the collected data, we could provide a maximum likelihood estimate: We can use with the parameter value to generate expected values for our data. For example: so we would expect observations for the number . The rest of the expected values are calculated similarly: Number Observation Expected Now we can calculate the statistic: With categories, it takes measurements to fully specify the data. Then, we used the data itself to estimate the value of one parameter, . So the number of degrees of freedom is , with critical value . Since , our data is not sufficiently different from expected to reject the hypothesis of a geometric distribution. " }, { "id": "exercises-Chi-Squared-1", @@ -1873,9 +1927,27 @@ var ptx_lunr_docs = [ "body": " Values 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 " }, { - "id": "backmatter-3", + "id": "app-Chi-squared-table", "level": "1", - "url": "backmatter-3.html", + "url": "app-Chi-squared-table.html", + "type": "Section", + "number": "B.1", + "title": "\\(\\chi^2\\)<\/span> Critical Values", + "body": " Critical Values Critical Values Degrees of Freedom Critical value for " +}, +{ + "id": "table-Chi-squared", + "level": "2", + "url": "app-Chi-squared-table.html#table-Chi-squared", + "type": "Table", + "number": "B.1.1", + "title": "\\(\\chi^2\\)<\/span> Critical Values", + "body": " Critical Values Degrees of Freedom Critical value for " +}, +{ + "id": "backmatter-4", + "level": "1", + "url": "backmatter-4.html", "type": "Colophon", "number": "", "title": "Colophon", diff --git a/my-great-book.html b/my-great-book.html index e1e627d..408e079 100755 --- a/my-great-book.html +++ b/my-great-book.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/sec-CLT.html b/sec-CLT.html index 3f234c4..d5df140 100755 --- a/sec-CLT.html +++ b/sec-CLT.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/sec-Chi-Squared.html b/sec-Chi-Squared.html index a04937f..bfe58d3 100755 --- a/sec-Chi-Squared.html +++ b/sec-Chi-Squared.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,21 +302,179 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon

    • Section 5.4 \(\chi^2\) Test

    -
    Text of section.
    🔗
    +
    In our previous hypothesis tests, we’ve asked about the correct value of some distribution parameter. But we might also be interested in whether a particular type of distribution fits the data in the first place. In this situation, we can try to measure the extent to which the observed data differs from what would be expected under a particular distribution.
    🔗
    -

    +

    +Definition 5.4.1. +

    +
    +
    Suppose \(O_1, \dotsc, O_n\) are observed data with expected values \(E_1, \dotsc, E_n\text{.}\) The \(\chi^2\) statistic is:
    +
    +\begin{gather*} +\chi^2 = \sum_{i=1}^n \frac{(O_i - E_i)^2}{E_i}. +\end{gather*} +
    +
    🔗
    +
    +
    🔗
    The expression \(O_i - E_i\) directly measures the difference between an observation and its expected value. However, if we simply summed up these differences, then one observation which is higher than its expected value and another that’s lower would have differences that cancel out. Squaring the term ensures that any difference contributes positively when summed together. And dividing by \(E_i\) ensures that the differences are expressed relative to the size of the expected value. A difference of \(0.1\) might sound like a small difference, but it would have a different interpretation if the expected value is \(100\) than if the expected value is \(0.01\text{.}\)
    🔗
    +
    +
    So the overall number \(\chi^2\) is designed to be a measurement of how much the observed data differs from expectation. It seems like \(\chi^2\) could be higher or lower simply as the result of the number of terms involved in the summation. How much difference is enough to reject the distribution which generated those expected values? It seems that it should depend on that number of terms.
    🔗
    +
    +

    +Definition 5.4.2. +

    +
    If the data collected fall into \(n\) categories, then we will say that there are \(n - 1\) degrees of freedom.
    🔗
    +
    +
    🔗
    Suppose our data comes from polling \(100\) respondents and arranging their responses into \(n\) categories. Then, if we know how many people fall into categories \(1, 2, \dotsc, n-1\text{,}\) we will automatically know how many people fall into the final category, simply because the total number of respondents is already known.
    🔗
    +
    +
    For each different number of degrees of freedom, there will be a different critical value of the \(\chi^2\) statistic, above which we’ll say that the data differs sufficiently from expectation for us to reject the distribution being tested. A table of critical \(\chi^2\) values is provided in Section B.1.
    🔗
    +
    +

    +Example 5.4.3. +

    +
    Suppose \(100\) people are surveyed about their favorite color among four choices. The results are below. Is this data consistent with the hypothesis that each of the four colors is equally likely to be a favorite?
    🔗
    +
    + + + + + + + + + + + + + + + + + + + + +
    ColorChosen as Favorite
    Blue\(37\)
    Green\(26\)
    Purple\(15\)
    Red\(22\)
    +
    In this case, if each color is equally likely to be a favorite, then we would expect \(25\) respondents to choose each color. So the \(\chi^2\) statistic is:
    +
    +\begin{gather*} +\chi^2 = \frac{(37 - 25)^2}{25} + \frac{(26 - 25)^2}{25} + \frac{(15 - 25)^2}{25} + \frac{(22 - 25)^2}{25} = 10.16. +\end{gather*} +
    +
    Since the data fall into four categories, the number of degrees of freedom is \(4 - 1 = 3\text{.}\) From the table in Table B.1.1, the critical value is \(7.815\text{.}\) Since \(10.16 \gt 7.815\text{,}\) our collected data is sufficiently different to reject the hypothesis of equal color preferences.
    +
    🔗
    +
    +
    🔗
    In the previous example, we’re testing an extrinsic hypothesis, i.e., a hypothesis made entirely without reference to the data. Knowing that we planned to poll \(100\) people, we could determine our expected values for this hypothesis before even conducting the survey. However, sometimes we need to use the collected data to estimate the value(s) of one or more parameters of a distribution. In such a situation, we say the hypothesis is intrinsic, and we adjust our calculation of degrees of freedom.
    🔗
    +
    +

    +Definition 5.4.4. +

    +
    Suppose it takes \(m\) measurements to fully specify the collected data, and suppose there are \(k\) parameters that are estimated using the data. Then the number of degrees of freedom is \(m - k\)
    🔗
    +
    +
    🔗

    +Example 5.4.5. +

    +
    Is the data below consistent with a geometric distribution?
    🔗
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    NumberObservation
    \(1\)\(59\)
    \(2\)\(21\)
    \(3\)\(11\)
    \(4\)\(8\)
    \(5\)\(1\)
    +
    In order to compare this data to a geometric distribution, we would need to know the value of the parameter \(\theta\) for the distribution. Based on the collected data, we could provide a maximum likelihood estimate:
    +
    +\begin{align*} +\widehat{\theta} \amp = \frac{59 + 21 + 11 + 8 + 1}{1 \cdot 59 + 2\cdot 21 + 3\cdot 11 + 4\cdot 8 + 5\cdot 1} \\ +\amp = \frac{100}{171} \\ +\amp \approx 0.58. +\end{align*} +
    +
    We can use Fact 2.1.14 with the parameter value \(0.58\) to generate expected values for our data. For example:
    +
    +\begin{align*} +g(2; 0.58) \amp = (1 - 0.58)^{1}(0.58) = 0.2436, +\end{align*} +
    +
    so we would expect \(0.2436 \times 100 = 24.36\) observations for the number \(2\text{.}\) The rest of the expected values are calculated similarly:
    +
    🔗
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    NumberObservationExpected
    \(1\)\(59\)\(58\)
    \(2\)\(21\)\(24.36\)
    \(3\)\(11\)\(10.23\)
    \(4\)\(8\)\(4.30\)
    \(5\)\(1\)\(1.80\)
    +
    Now we can calculate the \(\chi^2\) statistic:
    +
    +\begin{align*} +\chi^2 \amp = \frac{(59 - 58)^2}{58} + \dotsb + \frac{(1 - 1.8)^2}{1.8} \approx 4.08. +\end{align*} +
    +
    With \(5\) categories, it takes \(4\) measurements to fully specify the data. Then, we used the data itself to estimate the value of one parameter, \(\widehat{\theta}\text{.}\) So the number of degrees of freedom is \(4 - 1 = 3\text{,}\) with critical \(\chi^2\) value \(7.815\text{.}\) Since \(4.08 \lt 7.815\text{,}\) our data is not sufficiently different from expected to reject the hypothesis of a geometric distribution.
    +
    🔗
    +
    +
    🔗

    Exercises Exercises

    1.

    A store owner wants to determine how much shelf space to allocate to each of the drinks that they sell. They survey their customers about their favorite drinks. Is the data below consistent with the null hypothesis that each type of drink will be equally preferred?
    🔗
    -
    Table 5.4.1.
    🔗
    +
    Table 5.4.6.
    🔗
    @@ -337,7 +495,7 @@ eBookConfig.enable_chatcodes = false;
    A particular drug is administered in 100 independent trials. In each trial, the drug is administered to four people, and we count how many respond to the drug. The table below shows how many trials have each different count of people who respond to the drug.
    🔗
    -
    Table 5.4.2.
    🔗
    drink type water
    +
    Table 5.4.7.
    🔗
    diff --git a/sec-Conditional-Probability.html b/sec-Conditional-Probability.html index 38de418..3fec981 100755 --- a/sec-Conditional-Probability.html +++ b/sec-Conditional-Probability.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/sec-Confidence-Intervals.html b/sec-Confidence-Intervals.html index 50873d8..a3c5bd0 100755 --- a/sec-Confidence-Intervals.html +++ b/sec-Confidence-Intervals.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
  • +
    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • diff --git a/sec-Continuous-RVs.html b/sec-Continuous-RVs.html index d0d7290..1753718 100755 --- a/sec-Continuous-RVs.html +++ b/sec-Continuous-RVs.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Correlation.html b/sec-Correlation.html index fa491d0..1c9b9bb 100755 --- a/sec-Correlation.html +++ b/sec-Correlation.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Covariance.html b/sec-Covariance.html index b6e5c0d..7bb16b0 100755 --- a/sec-Covariance.html +++ b/sec-Covariance.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Discrete-RVs.html b/sec-Discrete-RVs.html index bd72df8..19b9789 100755 --- a/sec-Discrete-RVs.html +++ b/sec-Discrete-RVs.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Expected-Value.html b/sec-Expected-Value.html index 15ad3f8..d2fd61d 100755 --- a/sec-Expected-Value.html +++ b/sec-Expected-Value.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Independent-Events.html b/sec-Independent-Events.html index 9e74136..6af7fa0 100755 --- a/sec-Independent-Events.html +++ b/sec-Independent-Events.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    B \(\chi^2\) Critical Values Table
    + +
    • +
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    • diff --git a/sec-Introduction.html b/sec-Introduction.html index d7c2bb1..b9a2602 100755 --- a/sec-Introduction.html +++ b/sec-Introduction.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Joint-Distributions.html b/sec-Joint-Distributions.html index c3cfdf0..7152b54 100755 --- a/sec-Joint-Distributions.html +++ b/sec-Joint-Distributions.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Likelihood.html b/sec-Likelihood.html index ae3dd2b..4a2ee18 100755 --- a/sec-Likelihood.html +++ b/sec-Likelihood.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
  • Colophon
    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Linear-Regression.html b/sec-Linear-Regression.html index 8a8bc24..03488c1 100755 --- a/sec-Linear-Regression.html +++ b/sec-Linear-Regression.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-One-Sample-Tests.html b/sec-One-Sample-Tests.html index a2d6065..8c46d86 100755 --- a/sec-One-Sample-Tests.html +++ b/sec-One-Sample-Tests.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    + +
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    • diff --git a/sec-Power.html b/sec-Power.html index 38c6f5d..665ff0c 100755 --- a/sec-Power.html +++ b/sec-Power.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Probability.html b/sec-Probability.html index 9d87337..2d15181 100755 --- a/sec-Probability.html +++ b/sec-Probability.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    B \(\chi^2\) Critical Values Table
    + +
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    • diff --git a/sec-Set-Theory.html b/sec-Set-Theory.html index e08c092..ad52f31 100755 --- a/sec-Set-Theory.html +++ b/sec-Set-Theory.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    + +
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    • diff --git a/sec-Two-Sample-Tests.html b/sec-Two-Sample-Tests.html index ac0f295..f78ea29 100755 --- a/sec-Two-Sample-Tests.html +++ b/sec-Two-Sample-Tests.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    + +
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    • diff --git a/sec-Variance.html b/sec-Variance.html index e4affcf..72d1978 100755 --- a/sec-Variance.html +++ b/sec-Variance.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.19'; +eBookConfig.runestone_version = '7.12.2'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -302,7 +302,11 @@ eBookConfig.enable_chatcodes = false;
    A \(\Phi(z)\) Table
    -
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    • +
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    B \(\chi^2\) Critical Values Table
    + +
    • +
  • Colophon
    • # who respond to drug 0