Small business owners play a major role in the welfare of today’s economy. This particular segment has a reputation for working long hours during the week. Suppose the Small Business Administration (SBA), a federal agency charged with supporting small businesses, would like to test the hypothesis that full time small business owners average more than 5 hours per week at work when compared to part time small business owners. A random sample of 15 full time owners averaged 51.9 hours per week with a sample standard deviation of 5.5 hours per week. A random sample of 12 part time owners averaged 41.5 hours per week with a sample standard deviation of 5.2 hours per week. Assume the population variances for hours worked per week for both groups are equal.

a. Using α = 0.05, perform this hypothesis test for the SBA.

b. Approximate the p value using Table 5 in Appendix A and interpret the results.

c. Construct a 95% confidence interval to estimate the average difference in hours worked per week between these two groups. Interpret your result.

d. Determine the precise p value using Excel and interpret the results.

e. Verify your results using PHStat.

f. What assumptions need to be made in order to perform this procedure?