Students in many universities provide evaluations of their courses and professors. At a certain university, a simple random sample of 14 student evaluation scores of different female professors is taken with mean 4.0 and standard deviation 0.829. If another sample of 15 male professors has a mean score of 4.2 and standard deviation of 0.328 test the claim at the 0.05 significance level that female professors and male professors have different mean evaluation ratings.

a. State the null and alternative hypothesis

b. Manually calculate the test statistic and find the critical value from the table.

c. Test the claim using the critical value method

d. Test the claim by constructing an appropriate confidence interval.

e. Make a conclusion. Does there appear to be a difference in mean evaluation scores for male and female professors?