The average length of short hospital stays for men is slightly longer than that for women, 5.2

The average length of €œshort hospital stays€ for men is slightly longer than that for women, 5.2 days versus 4.5 days. A random sample of recent hospital stays for both men and women revealed the following. At α = 0.01, is there sufficient evidence to conclude that the average hospital stay for men is longer than the average hospital stay for women?

a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.

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MenWomen Sample size Sample mean 32 30 5.5 days 4.2 days Population standard deviation 2 days 1.5 days