The CEO of the company in Example 9 claims that the mean work day of the company’s mechanical engineers is less than 8.5 hours. A random sample of 25 of the company’s mechanical engineers has a mean work day of 8.2 hours. Assume the population standard deviation is 0.5 hour and the population is normally distributed. At α = 0.01, test the CEO’s claim.

a. Identify the claim and state H₀ and H_a.

b. Identify the level of significance α.

c. Find the critical value z₀ and identify the rejection region.

d. Find the standardized test statistic z. Sketch a graph.

e. Decide whether to reject the null hypothesis.

f. Interpret the decision in the context of the original claim.