1. Referring to sheet ‘Topic 1—Interval Estimates’ in the data file answer the following questions.

A. Based on the sample of 50 students, calculate the point estimate for the average $ that students spend on their cell phones and the standard deviation of that average. Make sure you’re using the right variable for this problem. There are two variables in the sheet, but only one makes sense to use.

B. Construct a 90% confidence interval around this point estimate. (Assume you don’t have a good estimate for the population standard deviation, so you have to estimate it using the sample standard deviation. Accordingly, make sure you use the t distribution when calculating the confidence interval.)

C. Interpret the results of part b). What does your interval estimate tell you?

D. Now assume your clients want a smaller confidence interval, with a margin of error that’s no bigger than 2$. How big would your new sample have to be? (Use the standard deviation you calculated in part A, as a planning value for the population standard deviation.)

Krash Drinkers	Non Krash Drinkers
84	65
85	69
86	70
87	74
89	73
70	77
75	80
77	85
54	68
68	95
78	50
79	54
	49

2. Referring to sheet ‘Topic 1—Interval Estimates’ in the data file, answer the following questions.

A. Based on the sample of 50 students, calculate the point estimate for the proportion of students who pay for their own cell phone plans.

B. Construct a 90% confidence interval around this point estimate.

C. Interpret the results of part b). What does your interval estimate tell you?

D. Now assume your client wants a smaller confidence interval, with a margin of error that’s no bigger than 5%. How big would your new sample have to be? (Use the proportion you calculated in part A, as a planning value for the proportion.)

Topic 2: Hypothesis Testing (Single Sample & Single Population)

The U.S. military awards the 'purple heart' award to all service members who are injured in the course of duty. Recently it was discovered that many soldiers who received concussions in the course of serving in Afghanistan and Iraq have not received purple hearts. (http://www.npr.org/2010/09/09/129606127/purple-hearts-elusive-for-traumatic-brain-injuries.)
The military wants to know how widespread this neglect is. In particular they want to know if fewer than 50 percent of soldiers with concussions have been awarded the purple heart. Unfortunately their records aren't computerized, so it would be prohibitively expensive to examine the records of every soldier who has received a concussion in the last ten years.
Instead they take a random sample of fifty soldiers who were recently diagnosed with concussions received in the line of duty and find that 23 of them received purple hearts. They approach you, and ask for your help looking into this issue.

A. Set up your research and null hypothesis, such that, if you reject the null hypothesis, you're asserting that fewer than 50% of all soldiers who were concussed in the line of duty received purple hearts.
(2 points)

B. Calculate the standard error and test statistic for this hypothesis test.
(2 points)

C. Calculate and interpret the p-value for this hypothesis test.
(4 points)

Topic 3: Hypothesis Testing (Two Samples Drawn from Two Populations)

1. The manufacturers of "Krash Cola" claim that students who drink Krash Cola before their statistics do better on their statistics exams. A group of Kwantlen marketing students decide to test this claim. They divide themselves into two groups - one group drinks Krash before their exam, while the other drinks only water. (You will find the results in the same excel file you opened for topic # 1, but in the second worksheet (called Topic 3- #1).)

They aren't sure what to make of the results, so they bring the data to you, and ask you if you think Krash appears to have a statistically significant effect on student performance.

a) Specify the null and alternate hypothesis that you would use, such that if you reject the null you’re concluding that Krash Cola does work.

b) What's the point estimate of the difference between the two groups' averages?

c) Assume the students want to be 90% certain before rejecting the null hypothesis. Can you reject the null hypothesis you established in 4a? Make sure your answer includes an interpretation of the p-value for this hypothesis test, as well as whether this is a one tailed or a two tailed test.

2. Based on your advice, the marketing students in # 1 conduct another study of the impact of Krash Cola. You've suggested they modify their study design to use a matched sample to examine the relationship between performance and Krash Cola consumption. They do so and return to you for help in the analysis. (You will find the results in the same excel file you opened for the last problem, but in the third worksheet – called Topic 3 -- # 2.)

a) What's the difference between a study which uses a matched sample design and one which uses an independent sample design? In the case of Krash Cola, why might you propose a matched sample study design?

b) Specify the null and alternate hypotheses that you would use, such that if you reject the null you’re concluding Krash Cola does work.

c) What's your point estimate of the average difference between the scores people got when they drank Krash Cola beforehand and the scores they got when they had not drank Krash Cola before hand?

d) Perform a hypothesis test, for a level of significance = .1. Find and interpret the p-value, and decide whether or not you can reject the null hypothesis.

e) Does your answer for this problem agree with your answer for #1? Would you expect it to? To what do you attribute any differences? Which result would you trust more and why?