A bottling company claims that the variance of the amount of sports drink in a 12-ounce bottle is no more than 0.40. A random sample of 31 bottles has a variance of 0.75. At α = 0.01, is there enough evidence to reject the company’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.