Question: A firm is considering requiring its secretaries to take a business typing class. 12 secretaries are randomly selected. Each is tested before (B) enrolling in the class, and then tested again 6 months after (A) passing the class. The following test results are reported in words per minute, adjusted for errors.

Secretary WPM Before WPM After

Alice 40 45
Bob 30 40
Carol 65 65
Daniel 70 65
Evelyn 45 50
Frank 45 40
Grace 55 55
Harry 60 65
Irene 75 75
Jack 35 40
Kathy 40 50
Larry 50 55

A. At the 5% level of significance, does the sample data indicate that the typing class improves typing performance? BE SURE TO INDICATE WHICH WAY YOU ARE SUBTRACTING.

B. Estimate the population mean difference with a 90% confidence interval estimate.

C. What are the advantages of using the same secretaries for both samples? What factors affecting typing performance might still not be accounted for using this procedure?

D. What is the p-value for your hypothesis test?

E. Perform the hypothesis test again, assuming that the samples are INDEPENDENT rather than dependent. Assume that the variances are equal and use FORMULA G from my Econ 262 Formulas handout (use the POOLED standard deviation).

F. What is the p-value for this second hypothesis test.