In a simple random sample of size 95 , there were 66 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 95 , there were 66 individuals in the category of interest. It is desired to test $H _ { 0 } : p = 0.78$   versus $H _ { 1 } : p < 0.78$ Do you reject $H _ { 0 }$ at the0.05  level?

Quizplus · Accepted Answer

To determine whether to reject $H_0$, calculate the test statistic using the formula for a proportion z-test: $ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} $, where $\hat{p} = \frac{66}{95} \approx 0.6947$, $p_0 = 0.78$, and $n = 95$. The calculated z-value is approximately -2.07. The critical z-value for a one-tailed test at the 0.05 level is -1.645. Since -2.07 < -1.645, we reject $H_0$.

In a Simple Random Sample of Size 95 , There H0:p=0.78H _ { 0 } : p = 0.78H0​:p=0.78

In a Simple Random Sample of Size 95 , There $H _ { 0 } : p = 0.78$