A nonprofit consumer organization says that the mean price of the vehicles the organization rated in a recent year is at least $41,000. In a random sample of 150 vehicles the organization rated in a recent year, the mean price is $40,600 and the standard deviation is $17,300. At α = 0.01, is there enough evidence to reject the organization’s claim?

For each exercise, perform the steps below.

(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.