Question

an education researcher claims that at most 8% of working college students are employed as teachers or teaching assistants. in a random sample of 500 working college students, 10% are employed as teachers or teaching assistants. at \\( \alpha = 0.10 \\), is there enough evidence to reject the researchers claim? complete parts (a) through (d) below. (a) identify the claim and state \\( h _ { 0 } \\) and \\( h _ { a } \\). identify the claim in this scenario. select the correct choice below and fill in the answer box to complete your choice. (type an integer or a decimal. do not round.) \\( \bigcirc \\) a. at most \\( \square \\% \\) of working college students are employed as teachers or teaching assistants \\( \bigcirc \\) b. the percentage of working college students who are employed as teachers or teaching assistants is not \\( \square \\% \\) \\( \bigcirc \\) c. \\( \square \\% \\) of working college students are employed as teachers or teaching assistants \\( \bigcirc \\) d. more than \\( \square \\% \\) of working college students are employed as teachers or teaching assistants

Explanation:

The researcher's claim is "at most 8% of working college students are employed as teachers or teaching assistants". In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality or no difference. The alternative hypothesis \(H_a\) is the statement we are trying to find evidence for.

Since the claim is about a proportion (\(p\)) being at most a certain value, the null hypothesis \(H_0\) will include the equality part of the claim. The alternative hypothesis \(H_a\) will be the opposite of the null hypothesis for a one - tailed test.

Answer:

A. At most \(8\%\) of working college students are employed as teachers or teaching assistants.

\(H_0:p\leq0.08\)

\(H_a:p > 0.08\)