In a typical month, men spend $178 and women spend $96 on leisure activities,” according to the results of an International Communications Research (ICR) for American Express poll, as reported in a USA Today Snapshot found on the Internet June 25, 2005. Suppose random samples were taken from the population of male and female college students. Each student was asked to determine his or her expenditures for leisure activities in the prior month. The sample data results had a standard deviation of $75 for the men and a standard deviation of $50 for the women.
a. If both samples were of size 20, what is the standard error for the difference of two means?
b. Assuming normality in leisure activity expenditures, is the difference found in the ICR poll significant at a = 0.05 if the samples in part a are used? Explain.