Math 207—More Large-Sample Significance Test Examples

Example 1 (Large-Sample Test of a Difference in Population Means)

A researcher is interested in salaries of economics assistant professors at 4-year U.S. universities. Specifically, he is interested in the difference between the mean male salary and the mean female salary. He suspects that the means are different. He takes random samples of male and female salaries and obtains the following results:

	Sample mean,	Sample standard deviation, s	Sample size, n
Males	43,172.7	13,069.8	50
Females	37,281.1	10,291.3	50

1. Carry out the significance test (state the hypotheses, check any conditions of the test, calculate the test statistic, calculate the p-value, and interpret the results). Are the results statistically significant at the 0.05 significance level?

2. Now find a 95% confidence interval for the difference in population mean salaries. How does this confidence interval relate to the analysis you performed in part a? Furthermore, what does this confidence interval tell you about the practical significance of the results?

Example 2 (Large-Sample Test of a Difference in Population Proportions)

A university financial aid office polled a random sample of undergraduate students in order to study the students’ summer employment. Given these data (shown below), is there evidence that the proportion of all male students employed during the summer is larger than the proportion of all females employed? Carry out the appropriate significance test (state the hypotheses, check any conditions of the test, calculate the test statistic, calculate the p-value, and interpret the results).

	Male students	Female students
Employed	718	593
Unemployed	79	139
Total	797	732