diff --git a/source/review/Exam-2-Review.ptx b/source/review/Exam-2-Review.ptx index 9b673e9..44bfa7c 100644 --- a/source/review/Exam-2-Review.ptx +++ b/source/review/Exam-2-Review.ptx @@ -28,7 +28,6 @@ -

@@ -114,8 +113,7 @@ - - +

Suppose we flip a coin 100 times and count 60 heads. @@ -273,7 +271,7 @@ - +

In each of the following scenarios, determine whether we should use a 1-tailed test or a 2-tailed test. @@ -360,7 +358,6 @@ -

@@ -384,102 +381,178 @@ + + +

+ Suppose we find a coin and wonder whether it's fair. + As a first test, we decide to flip the coin 200 times and count the number of heads, S. + What values of S 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? +

+ + + +

+ Suppose we have a coin which we suspect comes up heads more often than a fair coin would. + As a first test, we decide to flip the coin 200 times and count the number of heads, S. + What values of S 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? +

+ + + + + +

+ Suppose we find a six-sided die and wonder whether it's fair. + As a first test, we decide to roll the die 100 times and count the number of times it comes up 1. + The expected number of 1's is 50/3, with a variance of 125/9. +

+ + + +

- 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? + 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?

- - - - - - - 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. + 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?

- - - - - - - # 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 \theta = 0.7? -

- - + + +

+ Suppose that this die is weighted so that it rolls a 1 with probability 0.2. + What would be the power of our test? +

+ + - - -

- 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 \widehat{\theta} for the probability that a person will respond to the drug? -

- - + + +

+ Suppose we roll the die 100 times and see 23 1's. + Use the maximum likelihood value for the probability of rolling a 1 to calculate the power of the test. +

+ + + + + + +

+ Suppose a particular plant when grown outdoors has an average height of 39 in with a variance of 20 in^2. + We suspect that growing this plant in a greenhouse will increase its height. + We take the average height of a sample of 50 plants grown in a greenhouse. + What is the minimum average height of this sample that would be extreme enough to reject the null hypothesis of equal means at the p = 0.05 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? +

+ + + + + +

+ 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 the MLE value of \widehat{\theta}? -

- - - + + +

+ Is the data consistent with a binomial distribution with parameter \theta = 0.7? +

+ + + + + +

+ 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 \widehat{\theta} for the probability that a person will respond to the drug? +

+ + + + + + +

+ Is the data consistent with a binomial distribution with the MLE value of \widehat{\theta}? +

+ + + - \ No newline at end of file