In Exercise 8.20, we explored the average cost of lodging at three different hotel chains. We randomly select 50 billing statements from the computer databases of the Marriott, Westin, and Doubletree hotel chains, and record the nightly room rates. A portion of the sample data is shown in the table.

a. Before looking at the data, would you have any preconceived idea about the direction of the difference between the average room rates for these two hotels? If not, what null and alternative hypotheses should you test?
b. Use the critical value approach to determine if there is a significant difference in the average room rates for the Marriott and the Westin hotel chains. Use α = .01.
c. Find the p-value for this test. Does this p-value confirm the results of part b?

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Marriott Westin Sample Average (S) Sample Standard Deviation 150 17.2 165 22.5