A travel analyst claims the mean daily base price for renting a full-size or less expensive vehicle in Vancouver, Washington, is more than \($36.\) You want to test this claim. In a random sample of 40 full-size or less expensive vehicles available to rent in Vancouver, Washington, the mean daily base price is \($42.\)

Assume the population standard deviation is \($19.\) At α = 0.10, do you have enough evidence to support the analyst’s claim?

(a) Identify the claim and state H₀ and H_a.

(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.

(c) Choose one of the options.
Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic.
Option 2: Find the appropriate standardized test statistic and the P-value.

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.