Question

a marine biologist claims that the mean length of mature female pink seaperch is different in fall and winter. a sample of 15 mature female pink seaperch collected in fall has a mean length of 108 millimeters and a standard deviation of 9 millimeters. a sample of 8 mature female pink seaperch collected in winter has a mean length of 103 millimeters and a standard deviation of 8 millimeters. at \\( \alpha = 0.02 \\), can you support the marine biologists 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.
(a) identify the claim and state \\( h _ { 0 } \\) and \\( h _ { a } \\).
which is the correct claim below?
a. \the mean length of mature female pink seaperch is the same in fall and winter.\
b. \the mean length of mature female pink seaperch is different in fall and winter.\
c. \the mean length of mature female pink seaperch is greater in the winter than in the fall.\
d. \the mean length of mature female pink seaperch is greater in the fall than in the winter.\
what are \\( h _ { 0 } \\) and \\( h _ { a } \\)?
the null hypothesis, \\( h _ { 0 } \\), is \\( \mu _ { 1 } = \mu _ { 2 } \\). the alternative hypothesis, \\( h _ { a } \\), is \\( \mu _ { 1 } \
eq \mu _ { 2 } \\).
which hypothesis is the claim?
the null hypothesis, \\( h _ { 0 } \\)
the alternative hypothesis, \\( h _ { a } \\)

Explanation:

The problem is about hypothesis testing for the difference in means. The claim is the statement we are testing. The null hypothesis \(H_0\) is a statement of equality (\(\mu_1=\mu_2\)), and the alternative hypothesis \(H_a\) is a statement of inequality (\(\mu_1
eq\mu_2\)). Since the claim is that the means are different (which is what \(H_a\) represents), we check which hypothesis matches the claim.

Answer:

B. "The mean length of mature female pink seaperch is different in fall and winter."
The alternative hypothesis \(H_a\) (\(\mu_1
eq\mu_2\)) is the claim.