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

Quizplus · Accepted Answer

The sample proportion $\hat{p} = 0.3$, the claimed proportion $p = 0.5$, and $q = 1 - p = 0.5$. Plug these into the formula: $z = \frac{0.3 - 0.5}{\sqrt{\frac{0.5 \times 0.5}{1320}}} = \frac{-0.2}{\sqrt{\frac{0.25}{1320}}} = \frac{-0.2}{0.0138} \approx -14.53$.

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