A call center claims that the mean wait time for a customer to connect with a customer care executive is at most 2.5 minutes. A random sample of 35 calls at the call center has a mean wait time of 2.75 minutes and a standard deviation of 1.25 minutes. Is there enough evidence to reject the claim at α = 0.05?

(a) identify the claim and state H₀ and H_a,

(b) find the critical value(s) and identify the rejection region(s),

(c) find the standardized test statistic t,

(d) decide whether to reject or fail to reject the null hypothesis, and

(e) interpret the decision in the context of the original claim. Assume the population is normally distributed.