From previous studies, it is concluded that 10% of workers were employed from their college alumni program. A researcher claims that the proportion is smaller than 10% and decides to survey 500 working adults. Test the researcher's claim at the $\alpha = 0.01$ significance level.
Preliminary:
a. Is it safe to assume that $n \leq 0.05$ of all subjects in the population?
No
Yes
b. Verify $np(1 - p) \geq 10$. Round your answer to one decimal place.
$np(1 - p) =$
Test the claim:
a. The null and alternative hypotheses are
$H_0: p \leq 0.1$
$H_a: p > 0.1$
$H_0: \mu \geq 0.1$
$H_a: \mu < 0.1$
$H_0: \mu = 0.1$
$H_a: \mu \neq 0.1$
$H_0: \mu \leq 0.1$
$H_a: \mu > 0.1$
$H_0: p = 0.1$
$H_a: p \neq 0.1$
$H_0: p \geq 0.1$
$H_a: p < 0.1$
b. The test is
Select an answer
c. Based on the sample of 500 people, 4% workers were employed from their college alumni program.
What is the test statistic? Round your answer to two decimal places.
d. What is the $p$-value? Round your answer to four decimal places.
e. Make a decision.
Reject the null hypothesis.
Do not reject the null hypothesis.
f. Make a conclusion.
There is sufficient evidence that the proportion of people who workers were employed from their college alumni program is smaller than 10% at the $\alpha = 0.01$ significance level.
There is not sufficient evidence that the proportion of people who workers were employed from their college alumni program is smaller than 10% at the $\alpha = 0.01$ significance level.