A marine biologist claims that the mean length of mature female pink seaperch is different in fall and winter. A sample of 26 mature female pink seaperch collected in fall has a mean length of 127 millimeters and a standard deviation of 14 millimeters. A sample of 31 mature female pink seaperch collected in winter has a mean length of 117 millimeters and a standard deviation of 9 millimeters. At α = 0.01, can you support the marine biologist’s claim? Assume the population variances are equal.

(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,

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.