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 119 millimeters and a standard deviation of 11 millimeters. A sample of 10 mature female pink seaperch collected in winter has a mean length of 114 millimeters and a standard deviation of 8 millimeters. At alphaequals0.01​, 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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Part 1
​(a) Identify the claim and state Upper H 0 and Upper H Subscript a.
Which is the correct claim​ below?
A.
​"The mean length of mature female pink seaperch is greater in the fall than in the​ winter."
B.
​"The mean length of mature female pink seaperch is greater in the winter than in the​ fall."
C.
​"The mean length of mature female pink seaperch is different in fall and​ winter."
Your answer is correct.D.
​"The mean length of mature female pink seaperch is the same in fall and​ winter."
Part 2
What are Upper H 0 and Upper H Subscript a​?
The null​ hypothesis, Upper H 0​, is
mu 1 equals mu 2 .
The alternative​ hypothesis, Upper H Subscript a​, is
mu 1 not equals mu 2 .
Part 3
Which hypothesis is the​ claim?
The null​ hypothesis, Upper H 0
The alternative​ hypothesis, Upper H Subscript a
Your answer is correct.
Part 4
​(b) Find the critical​ value(s) and identify the rejection​ region(s).
Enter the critical​ value(s) below.