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# 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...

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 alpha = 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.