A sports statistician claims that the mean winning times for Boston Marathon women’s open division champions is at least 2.68 hours. The mean winning time of a sample of 30 randomly selected Boston Marathon women’s open division champions is 2.60 hours. Assume the population standard deviation is 0.32 hour. At α = 0.05, can you reject the 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.