An estate agent says that the mean rental of a warehouse (with basic amenities) is \($2,500.\) You suspect this claim is incorrect and find that a random sample of 38 such warehouses has a mean rental of \($2,850\) and a standard deviation of \($700.\) Is there enough evidence to reject the claim at α = 0.01?

(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.