sports statistician claims that the mean winning times for Boston Marathon women’s open division champions is at least 2.6 hours. The mean winning time of a sample of 30 randomly selected Boston Marathon women’s open division champions is 2.52 hours. Assume the population standard deviation is 0.18 hour. At a = 0.05, can you reject the claim?

(a) identify the claim and state \(H_{0}\) 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.