Question

a researcher claims that the stomachs of blue crabs from location a contain more fish than from location b. the stomach contents of a sample of 13 blue crabs from location a contai of fish and a standard deviation of 35 milligrams. the stomach contents of a sample of 7 blu contain a mean of 181 milligrams of fish and a standard deviation of 41 milligrams. at α=0. the researcher’s claim? assume the population variances are equal. complete parts (a) thro (a) identify the null and alternative hypotheses. choose the correct answer below. a. $h_0: mu_1 - mu_2 geq 0$ $h_a: mu_1 - mu_2 < 0$ b. $h_0: mu_1 - mu_2 = 0$ $h_a: mu_1 - mu_2
eq 0$ c. $h_0: mu_1 - mu_2 < 0$ $h_a: mu_1 - mu_2 = 0$ d. $h_0: mu_1 - mu_2 leq 0$ $h_a: mu_1 - mu_2 > 0$

Explanation:

The researcher claims that blue crabs from Location A have more fish in their stomachs than those from Location B. Let \(\mu_1\) be the mean for Location A and \(\mu_2\) for Location B. The null hypothesis (\(H_0\)) is the statement of no effect or the opposite of the claim, and the alternative hypothesis (\(H_a\)) is the researcher's claim. The claim is \(\mu_1-\mu_2 > 0\), so the null hypothesis should be \(H_0:\mu_1 - \mu_2\leq0\) (stating that Location A has less than or equal to Location B) and the alternative is \(H_a:\mu_1-\mu_2 > 0\), which matches option D.

Answer:

D. \(H_0:\mu_1 - \mu_2\leq0\)
\(H_a:\mu_1 - \mu_2>0\)