Update to PreTeXt project source.
This commit is contained in:
+159
-86
@@ -28,7 +28,6 @@
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</subsection>
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<exercises>
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<exercise>
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<statement>
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<p>
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@@ -114,8 +113,7 @@
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</task>
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</exercise>
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<exercise>
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<exercise>
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<statement>
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<p>
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Suppose we flip a coin 100 times and count 60 heads.
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@@ -273,7 +271,7 @@
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</answer>
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</exercise>
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<exercise>
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<exercise>
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<introduction>
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<p>
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In each of the following scenarios, determine whether we should use a 1-tailed test or a 2-tailed test.
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@@ -360,7 +358,6 @@
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</statement>
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</exercise>
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<exercise>
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<statement>
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<p>
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@@ -384,102 +381,178 @@
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</statement>
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</exercise>
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<exercise>
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<statement>
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<p>
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Suppose we find a coin and wonder whether it's fair.
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As a first test, we decide to flip the coin 200 times and count the number of heads, <m>S</m>.
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What values of <m>S</m> would be extreme enough to reject the null hypothesis of a fair coin? If the coin actually has a 0.6 probability of coming up heads, what is the power of this test?
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</p>
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</statement>
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</exercise>
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<exercise>
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<statement>
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<p>
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Suppose we have a coin which we suspect comes up heads more often than a fair coin would.
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As a first test, we decide to flip the coin 200 times and count the number of heads, <m>S</m>.
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What values of <m>S</m> would be extreme enough to reject the null hypothesis of a fair coin? If the coin actually has a 0.6 probability of coming up heads, what is the power of this test?
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</p>
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</statement>
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</exercise>
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<exercise>
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<introduction>
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<p>
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Suppose we find a six-sided die and wonder whether it's fair.
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As a first test, we decide to roll the die 100 times and count the number of times it comes up 1.
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The expected number of 1's is 50/3, with a variance of 125/9.
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</p>
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</introduction>
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<task>
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<statement>
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<p>
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A store owner wants to determine how much shelf space to allocate to each of the drinks that they sell.
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They survey their customers about their favorite drinks.
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Is the data below consistent with the null hypothesis that each type of drink will be equally preferred?
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Using a normal approximation, what is the smallest number of 1's greater than 50/3 that would be extreme enough to reject the null hypothesis of a fair die?
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</p>
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<table>
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<title></title>
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<tabular>
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<row header="yes" bottom="minor">
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<cell halign="center">drink type</cell>
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<cell halign="center">water</cell>
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<cell halign="center">soda</cell>
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<cell halign="center">tea</cell>
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<cell halign="center">coffee</cell>
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<cell halign="center">energy drinks</cell>
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</row>
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<row>
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<cell halign="center">favorite</cell>
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<cell halign="center">28</cell>
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<cell halign="center">17</cell>
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<cell halign="center">15</cell>
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<cell halign="center">26</cell>
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<cell halign="center">14</cell>
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</row>
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</tabular>
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</table>
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</statement>
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</exercise>
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</task>
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<exercise>
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<introduction>
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<task>
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<statement>
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<p>
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A particular drug is administered in 100 independent trials.
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In each trial, the drug is administered to four people, and we count how many respond to the drug.
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The table below shows how many trials have each different count of people who respond to the drug.
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Using a normal approximation, what is the greatest number of 1's less than 50/3 that would be extreme enough to reject the null hypothesis of a fair die?
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</p>
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<table>
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<title></title>
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<tabular>
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<row header="yes" bottom="minor">
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<cell halign="center"># who respond to drug</cell>
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<cell halign="center">0</cell>
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<cell halign="center">1</cell>
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<cell halign="center">2</cell>
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<cell halign="center">3</cell>
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<cell halign="center">4</cell>
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</row>
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<row>
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<cell halign="center"># of trials</cell>
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<cell halign="center">3</cell>
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<cell halign="center">11</cell>
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<cell halign="center">31</cell>
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<cell halign="center">34</cell>
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<cell halign="center">21</cell>
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</row>
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</tabular>
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</table>
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</introduction>
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</statement>
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</task>
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<task>
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<statement>
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<p>
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Is the data consistent with a binomial distribution with parameter <m>\theta = 0.7</m>?
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</p>
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</statement>
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</task>
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<task>
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<statement>
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<p>
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Suppose that this die is weighted so that it rolls a 1 with probability 0.2.
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What would be the power of our test?
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</p>
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</statement>
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</task>
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<task>
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<statement>
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<p>
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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 <m>\widehat{\theta}</m> for the probability that a person will respond to the drug?
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</p>
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</statement>
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</task>
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<task>
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<statement>
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<p>
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Suppose we roll the die 100 times and see 23 1's.
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Use the maximum likelihood value for the probability of rolling a 1 to calculate the power of the test.
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</p>
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</statement>
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</task>
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</exercise>
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<exercise>
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<statement>
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<p>
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Suppose a particular plant when grown outdoors has an average height of 39 in with a variance of 20 in<m>^2</m>.
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We suspect that growing this plant in a greenhouse will increase its height.
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We take the average height of a sample of 50 plants grown in a greenhouse.
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What is the minimum average height of this sample that would be extreme enough to reject the null hypothesis of equal means at the <m>p = 0.05</m> significance level? If the plants, when grown in a greenhouse, would truly have an average height of 41 in, what is the power of our test?
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</p>
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</statement>
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</exercise>
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<exercise>
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<statement>
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<p>
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A store owner wants to determine how much shelf space to allocate to each of the drinks that they sell.
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They survey their customers about their favorite drinks.
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Is the data below consistent with the null hypothesis that each type of drink will be equally preferred?
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</p>
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<table>
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<title></title>
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<tabular>
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<row header="yes" bottom="minor">
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<cell halign="center">drink type</cell>
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<cell halign="center">water</cell>
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<cell halign="center">soda</cell>
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<cell halign="center">tea</cell>
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<cell halign="center">coffee</cell>
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<cell halign="center">energy drinks</cell>
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</row>
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<row>
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<cell halign="center">favorite</cell>
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<cell halign="center">28</cell>
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<cell halign="center">17</cell>
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<cell halign="center">15</cell>
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<cell halign="center">26</cell>
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<cell halign="center">14</cell>
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</row>
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</tabular>
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</table>
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</statement>
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</exercise>
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<exercise>
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<introduction>
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<p>
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A particular drug is administered in 100 independent trials.
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In each trial, the drug is administered to four people, and we count how many respond to the drug.
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The table below shows how many trials have each different count of people who respond to the drug.
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</p>
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<table>
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<title></title>
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<tabular>
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<row header="yes" bottom="minor">
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<cell halign="center"># who respond to drug</cell>
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<cell halign="center">0</cell>
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<cell halign="center">1</cell>
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<cell halign="center">2</cell>
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<cell halign="center">3</cell>
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<cell halign="center">4</cell>
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</row>
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<row>
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<cell halign="center"># of trials</cell>
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<cell halign="center">3</cell>
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<cell halign="center">11</cell>
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<cell halign="center">31</cell>
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<cell halign="center">34</cell>
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<cell halign="center">21</cell>
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</row>
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</tabular>
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</table>
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</introduction>
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<task>
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<statement>
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<p>
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Is the data consistent with a binomial distribution with the MLE value of <m>\widehat{\theta}</m>?
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</p>
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</statement>
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</task>
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</exercise>
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<task>
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<statement>
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<p>
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Is the data consistent with a binomial distribution with parameter <m>\theta = 0.7</m>?
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</p>
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</statement>
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</task>
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<task>
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<statement>
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<p>
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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 <m>\widehat{\theta}</m> for the probability that a person will respond to the drug?
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</p>
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</statement>
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</task>
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<task>
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<statement>
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<p>
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Is the data consistent with a binomial distribution with the MLE value of <m>\widehat{\theta}</m>?
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</p>
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</statement>
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</task>
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</exercise>
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</exercises>
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</section>
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