The university registrar claims that fewer than 20 percent of undergraduate students stay in residence for their four years as students. To test this claim, a random sample of 100 graduating students was selected, and 18 were found to have lived in residence for their four years.
-The appropriate test statistic to test the hypotheses is _____.
A)5.00
B)0.50
C)0.212
D)-0.50
E)-1.00

Question

Quizplus · Accepted Answer

The test statistic for this hypothesis test is calculated using the formula for a proportion z-test: $ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} $, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{18}{100} = 0.18$, $p_0 = 0.20$, and $n = 100$. Plugging these values into the formula gives $ z = \frac{0.18 - 0.20}{\sqrt{\frac{0.20(0.80)}{100}}} = -0.50 $.

The University Registrar Claims That Fewer Than 20 Percent of Undergraduate