Question Set 1: Pennsylvania State Residency by Campus

Researchers are comparing the proportion of Penn State University Park students who are Pennsylvania residents to the proportion of Penn State World Campus students who are Pennsylvania residents. Data from a random sample are presented in the contingency table below.

Primary Campus

University Park

World Campus

Pennsylvania Resident

Yes

62

40

No

54

55

A. Construct a 95% confidence interval to estimate the difference between the proportion of all University Park students who are Pennsylvania residents and the proportion of all World Campus students who are Pennsylvania residents. If assumptions are met, use the normal approximation method. Explain how you checked assumptions. Use Minitab Express; you should not need to do any hand calculations. Remember to copy+paste all relevant Minitab Express output and to clearly identify your answers. [15 points]

B. Interpret the confidence interval you computed in part A by completing the following sentence. [5 points]

I am 95% confident that...

C. Use the five-step hypothesis testing procedure given below to determine if there is evidence of a difference between the proportion of University Park students who are Pennsylvania residents and the proportion of World Campus students who are Pennsylvania residents. If assumptions are met, use the normal approximation method. Use Minitab Express; you should not need to do any hand calculations. Remember to copy+paste all relevant Minitab Express output and to clearly identify your answers. [25 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p-value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion

Question Set 2: Mathematical Reasoning Skills by Curriculum

A large school district is considering changing their kindergarten mathematics curriculum. Before making any major changes, they first want to collect data to compare the outcomes of the two curricula. They have obtained a representative sample of 70 kindergarten students and randomly assigned each to be taught with either the new or old curriculum. After one year of instruction, all students completed an assessment of mathematical reasoning skills. Summarized sample data are presented in the table below.

Curriculum

N

Mean

SD

New

36

89.7

4.5

Old

34

86.1

5.1

A. Construct a 95% confidence interval to estimate the mean difference in the mathematical reasoning scores of the two groups. Use Minitab Express; you should not need to do any hand calculations. Remember to copy+paste all relevant Minitab Express output and to clearly identify your answers. [15 points]

B. Use the five-step hypothesis testing procedure given below to determine if there is evidence that the mean mathematical reasoning scores are different in the population. If assumptions are met, conduct a t test. Use Minitab Express; you should not need to do any hand calculations. Remember to copy+paste all relevant Minitab Express output and to clearly identify your answers. [25 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion

C. Compute Cohen's d for the difference in the two sample means. You will need to do calculations by hand. Remember to show all work. [10 points]

For a review of Cohen's d see page 6.4 of the online course notes.

D. Interpret the value of Cohen's d that you computed in part C. [5 points]