Think about the proportion of students at your college who are wearing clothing that displays the college name or logo today. Also suppose that a friend of yours attends a different college, and the two of you have a recurring discussion about which college displays more school pride. You decide to measure school pride by the proportion of students at the college who wear clothing that displays the college name or logo on a particular day. You want to investigate whether this proportion differs between your college (call it Exemplary Students University, ESU) and your friend’s college (call it Mediocre Students University, MSU).
Suppose that you find that 24% of a random sample of students at ESU wears clothing with the school name or logo, compared to 16% of a random sample of students at MSU. Our research question: Is the observed difference in percentage of students wearing school clothing at ESU versus MSU statistically significant?

1. Which of the following is the appropriate null hypothesis?

In general, the percentage of ESU students who wear school clothing is the same as that of MSU students.

In general, the percentage of ESU students who wear school clothing is different from that of MSU students.

In general, a smaller percentage of ESU students wear school clothing compared to MSU students.

In general, a greater percentage of ESU students wear school clothing compared to MSU students.

2. Which of the following is the appropriate alternative hypothesis?

In general, a smaller percentage of ESU students wear school clothing compared to MSU students.

In general, the percentage of ESU students who wear school clothing is the same as that of MSU students.

In general, the percentage of ESU students who wear school clothing is different from that of MSU students.

In general, a greater percentage of ESU students wear school clothing compared to MSU students.

3. Calculate an appropriate statistic value to compare ESU students to MSU students with regard to wearing school clothing.

4. What additional information do you need in order to assess whether this difference calculated in part (c) is statistically significant?

Difference in population sizes between the two schools.

Sample size in each group

Population size of all ESU and MSU students

Proportion of students in each group

5. Describe a scenario, involving the additional information you cited in part (d), in which you believe that this difference would be statistically significant.

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6. Describe a scenario, involving the additional information you cited in part (d), in which you believe that this difference would be NOT statistically significant. Choose the answer from the menu in accordance to the question statement

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