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.
(b) find the critical value(s) and identify the rejection region(s).
identify the critical value(s) for this test.
\\( z _ { 0 } = 1.28 \\)
(round to two decimal places as needed. use a comma to separate answers as needed.)
identify the rejection region(s). select the correct choice below and fill in the answer box(es) to complete your choice.
(round to two decimal places as needed)
(c) find the standardized test statistic z
\\( z = \square \\)
(round to two decimal places as needed)

Explanation:

Step1: Calculate \( \hat{p} \), \( p \), \( q \) and \( n \)

Given \( \hat{p}=0.10\), \(p = 0.08\), \(q=1 - p=0.92\), \(n = 500\)

Step2: Use the formula for the z - statistic in a proportion test

The formula for the z - statistic in a proportion test is \(z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}\)
Substitute the values:

$$
LATEXBLOCK0
$$

Answer:

\(z\approx1.65\)