An analyst claims that the mean annual salary for intermediate level architects in Wichita, Kansas, is more than the national mean, $52,000. The annual salaries (in dollars) for a random sample of 21 intermediate level architects in Wichita are listed. Assume the population is normally distributed and the population standard deviation is $8000. At α = 0.09, is there enough evidence to support the analyst’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.