A police chief claims that the standard deviation of the lengths of response times is less than 3.7 minutes. A random sample of 9 response times has a standard deviation of 3.0 minutes. At α = 0.05, is there enough evidence to support the police chief’s claim? Assume the population is normally distributed.

a. Identify the claim and state H₀ and H_a.

b. Identify the level of significance α and the degrees of freedom.

c. Find the critical value X₀² and identify the rejection region.

d. Find the standardized test statistic X².

e. Decide whether to reject the null hypothesis. Use a graph if necessary.

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