Question: A consulting agency was asked by a large insurance company to investigate if business majors were better salespersons than those with other majors. A sample of 20 salespersons with a business degree showed that they sold an average of 11 insurance policies per week. Another sample of 25 salespersons with a degree other than business showed that they sold an average of 9 insurance policies per week.
Assume that the two populations are normally distributed with population standard deviations of 1.80 and 1.35 policies per week, respectively.
a. Construct a 99% confidence interval for the difference between the two population means.
b. Using the 1% significance level, can you conclude that persons with a business degree are better salespersons than those who have a degree in another area?