Find the value of the test statistic z using $z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }$
A claim is made that the proportion of children who play sports is less than 0.5 , and the sample statistics include n=1320 subjects with 30 % saying that they play a sport.
A) 14.53
B) 29.66
C) -29.66
D) -14.53

Question

Find the value of the test statistic z using $z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }$ 
A claim is made that the proportion of children who play sports is less than  0.5 , and the sample statistics include  n=1320  subjects with  30 %  saying that they play a sport.
A)  14.53 
B)  29.66 
C)  -29.66 
D)  -14.53

Quizplus · Accepted Answer

Given $p = 0.5$, $\hat{p} = 0.3$, $q = 1 - p = 0.5$, and $n = 1320$, the test statistic $z$ is calculated as follows:$$z = \frac{\hat{p} - p}{\sqrt{\frac{pq}{n}}} = \frac{0.3 - 0.5}{\sqrt{\frac{(0.5)(0.5)}{1320}}} = \frac{-0.2}{\sqrt{\frac{0.25}{1320}}} = \frac{-0.2}{\sqrt{0.00018939}} = \frac{-0.2}{0.01376} = -14.53.$$This indicates that the sample proportion is 14.53 standard deviations below the hypothesized proportion, supporting the claim that fewer children play sports than the hypothesized proportion of 0.5.

Find the Value of the Test Statistic Z Using z=p^−ppqnz = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }z=npq​​p^​−p​

Find the Value of the Test Statistic Z Using $z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }$