A random sample of 100 medical school applicants at a university has a mean total score of 502 on the MCAT. According to a report, the mean total score for the school’s applicants is more than 499. Assume the population standard deviation is 10.6. At α = 0.01, is there enough evidence to support the report’s claim?

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

(b) Find the standardized test statistic z.

(c) Find the corresponding 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.