A marine biologist claims that the mean length of mature female pink seaperch is different in fall and winter. A sample of 12 mature female pink seaperch collected in fall has a mean length of 115 millimeters and a standard deviation of 11 millimeters. A sample of 10 mature female pink seaperch collected in winter has a mean length of 106 millimeters and a standard deviation of 8 millimeters. At α=0.01, can you support the marine biologist's claim? Assume the population variances are equal. Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e) below.
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