A researcher claims that the stomachs of blue crabs from Location A contain more
ID: 3067080 • Letter: A
Question
A researcher claims that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B. The stomach contents of a sample of
16 blue crabs from Location A contain a mean of 194 milligrams of fish and a standard deviation of 37milligrams. The stomach contents of a sample of 10 blue crabs from Location B contain a mean of 185 milligrams of fish and a standard deviation of 43 milligrams. At alpha?equals=0.050, can you support the? researcher's claim? Assume the population variances are equal. Complete parts? (a) through? (d) below.
A.) Identify the null and alternative hypotheses
B.) Find the standardized test statistic.
C.) Calculate the? P-value.
D.) State the conclusion.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: ?1< ?2
Alternative hypothesis: ?1 > ?2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 16.4457
DF = 24
t = [ (x1 - x2) - d ] / SE
t = 0.547
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 0.547
Therefore, the P-value in this analysis is 0.295.
Interpret results. Since the P-value (0.295) is greater than the significance level (0.05), we have to reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B.
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