A marine biologist claims that the mean length of mature female pink seaperch is different in fall and winter. A sample of 18 mature female pink seaperch collected in fall has a mean length of 110 millimeters and a standard deviation of 10 millimeters. A sample of 8 mature female pink seaperch collected in winter has a mean length of 96 millimeters and a standard deviation of 14 millimeters. At alpha=0.20 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.
(b)Find critical values and identify rejection region
(c) Find the standardized test statistic
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim
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