Question

Slot machines are the favorite game at casinos throughout the United States (Harrah’s Survey 2002: Profile of the American Gambler). A local casino wants to estimate the difference in the percent of women and me who prefer the slots with a 95% level of confidence. Random samples of 320 women and 250 men found that 256 women prefer slots and 165 men prefer slots.

1-

-Hypothesis test for one population mean (unknown population standard deviation)

2-Confidence interval estimate for one population mean (unknown population standard deviation)

3-Hypothesis test for population mean from paired differences

4-Confidence interval estimate for population mean from paired differences

5-Hypothesis test for difference in population means from two independent samples

6-Confidence interval estimate for difference in population means from two independent samples

7-Hypothesis test for one population proportion

8-Confidence interval estimate for one population proportion

9-Hypothesis test for difference between two population proportions

10-Confidence interval estimate for difference between two population proportions

The National Endowment for the Humanities sponsors summer institutes to improve the skills of high school language teachers. One institute hosted 20 French teachers for four weeks. At the beginning of the period, the teachers took the Modern Language Association's listening test of understanding of spoken French. After four weeks of immersion in French in and out of class, they took the listening test again. (The actual spoken French in the two tests was different, so that simply taking the first test should not improve the score on the second test.) The Director of the summer institute would like to estimate the change (and hopeful improvement) in the teachers' skills after participating in the class.

1-

-Hypothesis test for one population mean (unknown population standard deviation)

2-Confidence interval estimate for one population mean (unknown population standard deviation)

3-Hypothesis test for population mean from paired differences

4-Confidence interval estimate for population mean from paired differences

5-Hypothesis test for difference in population means from two independent samples

6-Confidence interval estimate for difference in population means from two independent samples

7-Hypothesis test for one population proportion

8-Confidence interval estimate for one population proportion

9-Hypothesis test for difference between two population proportions

10-Confidence interval estimate for difference between two population proportions

Answer 1

Answer a. 9 - Confidence interval estimate for difference between two population proportions

Explanation: Since an estimate of difference in the percentage (or proportion) of women and men who prefer slots is required, so we use interval estimation by finding 95% Confidence Interval for this difference.

Answer b. 4 - Confidence interval estimate for population mean from paired differences

Explanation: Here again the Director wants to estimate the change in the teachers' skills after participating in the class.

The same group of 20 teachers are exposed to the listening test before taking the classes and after taking the classes, so this corresponds to finding the difference in the paired scores of teachers. We take paired t-test because here one-to-one relationship is being identified i.e. the pre-score of a teacher can correspond to the post score of her test only and cannot correspond to the post test score of any other teacher.