In a simple random sample of size 88 , there were 22 individuals in the category of interest. It is desired to test $H _ { 0 } : p = 0.31$ versus $H _ { 1 } : p

Question

In a simple random sample of size 88 , there were 22 individuals in the category of interest. It is desired to test $H _ { 0 } : p = 0.31$ versus $H _ { 1 } : p < 0.31$. Compute the test statistic $z$
A) 0.05
B) -1.22
C) 0.25
D) 4.97

Quizplus · Accepted Answer

The test statistic $z$ is calculated using the formula $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{22}{88} = 0.25$, $p_0 = 0.31$, and $n = 88$. Plugging these values into the formula gives $z = \frac{0.25 - 0.31}{\sqrt{\frac{0.31(1-0.31)}{88}}} = -1.22$.

In a Simple Random Sample of Size 88 , There H0:p=0.31H _ { 0 } : p = 0.31H0​:p=0.31

In a Simple Random Sample of Size 88 , There $H _ { 0 } : p = 0.31$