Statistics Exam

Good luck on this exam and on all of your finals.

1. (25 pts)Worsted College conducted a survey two years in a row, year 1 (before COVID) and year 2 (after COVID) and asked students if, before their final exams, they accepted exam answers prepared by a star student, would that be considered cheating. All students surveyed in year 1 attended oncampus classes, all students surveyed in year 2 were studying online or remotely. Here is the actual question and the results:

“Suppose that a friend offers you exam answers prepared by a star student and you accept the prepared answers.” Do you consider this cheating?

	Yes, I consider it cheating	No, I do not consider it cheating	TOTAL
Pre-COVID survey	375	145
Post-COVID survey	325	135
TOTAL

You want to test if Post-COVID students are more relaxed about cheating. In other words, are Year 1 students more likely to consider the above scenario cheating than Year 2 students?

a. State your hypothesis in correct, formal notation. DEFINE YOUR VARIABLES.

b. Create a randomization for a hypothesis test for this data, and estimate the standard error of your distribution.

SE =

c. Use your randomization to test your hypotheses at the 𝛼𝛼 = 0.5 level of significance. Make sure you describe all steps and whether or not you reject the null hypothesis.

d. Interpret your conclusion in the context of the original problem.

e. Upload a screenshot of your StatKey screen that shows your standard error, your summary statistics, and your test.

f. Do the survey results imply any course of action by colleges and universities? If so, what would you suggest? If not, why not?

2. (25 pts)The Census Bureau publishes the American Community Survey

(EmployedACS) dataset that includes Income, ages and salary in thousands of dollars for males and females. (The Sex variable is coded 0 for female and 1 for male.) You are interested in the difference in mean income between women and men. Note that StatKey puts women into group 1 and men into group 2, so that x1 =xw .

a. Use StatKey to generate a bootstrap distribution for this sample. (Use the drop-down menu to access the sample.) What is the mean of the original sample?

b. What is the mean of your bootstrap distribution?

c. Use the bootstrap distribution to find a 92% confidence interval for the difference in mean income for males and females. Round to 3 decimal places.

e. Interpret your confidence interval.

f. Based on your confidence interval, is it likely that, on average, men and women earn the same? Explain in detail.

g. Upload a screenshot of your bootstrap distribution. Make sure your confidence interval and original sample information are displayed.

3. (20 pts)Stanley’s friend Maxine says she is REALLY gifted in writing. To demonstrate just how gifted she is, Maxine compares her SAT writing score of 760 to the scores of other students who took the test. The writing scores from the population of all students who took the SAT form a bell-shaped curve with mean 487 and standard deviation 115.

x−µ

a. Calculate Maxine’s z-score, z= for her writing SAT, rounding to 3 decimal places.

σ

b. Place Maxine’s z-score in the correct location along the horizontal axis in the graph below and shade in the region that represents Maxine’s p-value.

c. Use StatKey to determine Maxine’s p-value. Round to 4 decimal places.

d. Explain, in your own words, the meaning of Maxine’s p-value.