Question

a personnel director in a particular state claims that the mean annual income is greater in one of the state’s counties (county a) than it is in another county (county b). in county a, a random sample of 17 residents has a mean annual income of $42,400 and a standard deviation of $8900. in county b, a random sample of 8 residents has a mean annual income of $38,000 and a standard deviation of $5100. at α = 0.05, answer parts (a) through (e). assume the population variances are not equal. if convenient, use technology to solve the problem.

(a) identify the claim and state ( h_0 ) and ( h_a ).

which is the correct claim below?
a. \the mean annual income in county a is greater than in county b.\
b. \the mean annual incomes in counties a and b are equal.\
c. \the mean annual income in county a is less than in county b.\
d. \the mean annual incomes in counties a and b are not equal.\

what are ( h_0 ) and ( h_a )?

the null hypothesis, ( h_0 ), is dropdown. the alternative hypothesis, ( h_a ), is dropdown.

Explanation:

The claim is that the mean annual income in County A is greater than in County B. For hypothesis testing, the null hypothesis (\(H_0\)) is a statement of no difference or equality, and the alternative hypothesis (\(H_a\)) is the claim we are trying to find evidence for. So \(H_0\) should be that the mean of A is less than or equal to the mean of B (\(\mu_A \leq \mu_B\)) and \(H_a\) is that the mean of A is greater than the mean of B (\(\mu_A > \mu_B\)).

Answer:

The correct claim is A. "The mean annual income in county A is greater than in county B."
\(H_0\): \(\mu_A \leq \mu_B\)
\(H_a\): \(\mu_A > \mu_B\)