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 \text { 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 $H _ { 0 } : p = 0.31 \text { versus } H _ { 1 } : p < 0.31$ . Compute the test statistic z.
A) 0.05
B) -1.22
C) 0.25
D) 4.97

Quizplus · Accepted Answer

We have proportion of success p = 0.31, sample proportion of success $\hat { p }$ = 22/88 = 0.25, sample size n = 88.

$$z=\frac {\hat { p }-p}{\sqrt { \frac { p ( 1-p ) }{ n } } }=\frac{0.25-0.31}{\sqrt{\frac{0.31(1-0.31)}{88}}}\approx -1.22$$

Therefore, the test statistic z is approximately -1.22.

In a Simple Random Sample of Size 88, There Were H0:p=0.31 versus H1:p<0.31H _ { 0 } : p = 0.31 \text { versus } H _ { 1 } : p < 0.31H0​:p=0.31 versus H1​:p<0.31

In a Simple Random Sample of Size 88, There Were $H _ { 0 } : p = 0.31 \text { versus } H _ { 1 } : p < 0.31$