A factory hiring people for tasks on its assembly line gives applicants a test of manual dexterity. This test counts how many oddly shaped parts the applicant can install on a model engine in a one-minute period. Assume that these tested applicants represent simple random samples of men and women who apply for these jobs.
(a) Find 95% confidence intervals for the expected number of parts that men and women can install during a one-minute period.
(b) These data are counts, and hence cannot be negative or fractions. How can we use the normal model in this situation?
(c) Your intervals in part (a) should overlap. What does it mean that the intervals overlap?
(d) Find the 95% confidence interval for the difference μ men - μ women.
(e) Does the interval found in part (d) suggest a different conclusion about μ men - μ women than the use of two separate intervals?
(f) Which procedure is the right one to use if we’re interested in making an inference about μ men - μ women?