Question

an education researcher claims that at most 8% of working college students are employed as teachers assistants. in a random sample of 300 working college students, 9% are employed as teachers or teach α = 0.05, is there enough evidence to reject the researcher’s claim? complete parts (a) through (d) belo (a) identify the claim and state h₀ and hₐ. identify the claim in this scenario. select the correct choice below and fill in the answer box to complete (type an integer or a decimal. do not round.) a. at most % of working college students are employed as teachers or teaching assistants. b. more than % of working college students are employed as teachers or teaching assistants. c. the percentage of working college students who are employed as teachers or teaching assistar d. % of working college students are employed as teachers or teaching assistants. let p be the population proportion of successes, where a success is a working college student who is e teacher or teaching assistant. state h₀ and hₐ. select the correct choice below and fill in the answer b your choice. (round to two decimal places as needed.) a. h₀: p ≤ hₐ: p > b. h₀: p ≥ hₐ: p < c. h₀: p > hₐ: p ≤

Explanation:

Step1: Identify the claim

The researcher's claim is "at most 8% of working college students are employed as teachers or teaching assistants". So for the first part (identifying the claim), option A is correct with the percentage being 8. So we fill 8 in the box for option A.

Step2: State \(H_0\) and \(H_a\)

The null hypothesis \(H_0\) should match the claim (since the claim is a statement of no effect or the status - quo). The claim is "at most 8%", which in terms of proportion \(p\) (where \(p\) is the proportion of working college students employed as teachers or teaching assistants) is \(p\leq0.08\) (since 8% = 0.08). The alternative hypothesis \(H_a\) is the opposite of the null hypothesis when we are testing to reject the claim. Since we want to see if there is evidence that the proportion is more than 8% (to reject the "at most" claim), \(H_a:p > 0.08\). So for the hypothesis testing part, option A is correct with \(H_0:p\leq0.08\) and \(H_a:p > 0.08\). So we fill 0.08 in the boxes for \(H_0\) and \(H_a\) in option A.

Answer:

• For identifying the claim: A. At most \(\boldsymbol{8}\%\) of working college students are employed as teachers or teaching assistants.
• For stating \(H_0\) and \(H_a\): A. \(H_0:p\leq\boldsymbol{0.08}\), \(H_a:p > \boldsymbol{0.08}\)