$$\text { Find the value of the test statistic } z \text { using } z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } } \text {. }$$
-A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n = 1158 subjects with 30% saying that they play a sport.
A)27.78
B)13.61
C)-27.78
D)-13.61

Question

Quizplus · Accepted Answer

The test statistic $z$ is calculated using the formula $z = \frac{\hat{p} - p}{\sqrt{\frac{pq}{n}}}$, where $\hat{p} = 0.3$ (sample proportion), $p = 0.5$ (population proportion), $q = 1 - p = 0.5$, and $n = 1158$. Plugging these values into the formula gives $z = \frac{0.3 - 0.5}{\sqrt{\frac{(0.5)(0.5)}{1158}}} = -13.61$.

Find the value of the test statistic z using z=p^−ppqn. \text { Find the value of the test statistic } z \text { using } z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } } \text {. } Find the value of the test statistic z using z=npq​​p^​−p​.

$\text { Find the value of the test statistic } z \text { using } z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } } \text {. }$