For the following exercises where applicable:

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.
Use the traditional method of hypothesis testing unless otherwise specified. Assume all variables are normally distributed.

A travel agent claims that the average of the number of rooms in hotels in a large city is 500. At α = 0.01, is the claim realistic? The data for a random sample of seven hotels are shown.

713     300     292     311     598     401     618

Give a reason why the claim might be deceptive.