Productivity. A bakery hiring people to make bread gives job applicants a test of speed. This test counts how many loaves of bread each applicant can bake in a 10-minute period. The following table summarizes the data by gender of the job applicant. Assume that all conditions necessary for inference are met.

Male Female Number of Subjects 40 40 Loaves baked:
Mean 23.4 24.9 SD 2.54 2.98

a) Find 95% confidence intervals for the average number of loaves that each gender can make.

b) Those intervals overlap. What does this suggest about any gender-based difference in speed?

c) Find a 95% confidence interval for the difference in the mean number of loaves that can be baked by men and women.

d) What does this interval suggest about any gender-based difference in speed?

e) The two results seem contradictory. Which method is correct: doing two-sample inference, or doing one-sample inference twice?

f) Why don’t the results agree?