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. teachers or teaching assistants. b. the percentage of working college students who are employed as teachers or teaching assistants is not % c. % of working college students are employed as teachers or teaching assistants. d. more than % 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 employed as a teacher or teaching assistant. state \\( h _ { 0 } \\) and \\( h _ { a } \\). select the correct choice below and fill in the answer boxes to complete your choice. (round to two decimal places as needed.) a. \\( h _ { 0 } : p \leq 0.08 \\) b. \\( h _ { 0 } : p \
eq \\) c. \\( h _ { 0 } : p < \\) \\( h _ { a } : p > 0.08 \\) \\( h _ { a } : p = \\) \\( h _ { a } : p \geq \\) d. \\( h _ { 0 } : p > \\) e. \\( h _ { 0 } : p = \\) f. \\( h _ { 0 } : p \geq \\) \\( h _ { a } : p \leq \\) \\( h _ { a } : p \
eq \\) \\( h _ { a } : p < \\) (b) find the critical value(s) and identify the rejection region(s). identify the critical value(s) for this test. \\( z _ { 0 } = \\) (round to two decimal places as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Determine the type of test

Since \(H_{a}:p > 0.08\), this is a right - tailed test.

Step2: Find the critical value

For a right - tailed test with \(\alpha=0.10\), we look up the \(z\) - value in the standard normal distribution table. The critical value \(z_{0}\) is the value such that \(P(Z>z_{0})=\alpha = 0.10\), which is equivalent to \(P(Z\leq z_{0})=1 - 0.10=0.90\).
Looking up in the standard normal table (or using a calculator with a normal distribution function, e.g., \(z=\text{NORM.S.INV}(0.9)\)), we get \(z_{0}=1.28\)

Answer:

\(z_{0}=1.28\)