In a simple random sample of size 73, there were 44 individuals in the category of interest. It is desired to test $H _ { 0 } : p = 0.78$
versus $H _ { 1 } : p

Question

In a simple random sample of size 73, there were 44 individuals in the category of interest. It is desired to test $H _ { 0 } : p = 0.78$
versus $H _ { 1 } : p < 0.78$
Compute the test statistic  z .
A)  0.60 
B)  -3.65 
C)  0.05 
D)  8.68

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, $\hat{p} = \frac{44}{73}$, $p_0 = 0.78$, and $n = 73$. Plugging these values into the formula gives $z = \frac{\frac{44}{73} - 0.78}{\sqrt{\frac{0.78(1-0.78)}{73}}}$, which calculates to approximately -3.65.

In a Simple Random Sample of Size 73, There Were H0:p=0.78H _ { 0 } : p = 0.78H0​:p=0.78

In a Simple Random Sample of Size 73, There Were $H _ { 0 } : p = 0.78$