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.
14.53
$-14.53$
29.66
$-29.66$

Answer

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Answer

The correct answer is $\boxed{-14.55}$

Steps

Step 1 ：Substitute the given values into the formula: $z = \frac{\hat{p} - p}{\sqrt{\frac{p q}{n}}}$

Step 2 ：Substitute $n = 1320$, $\hat{p} = 0.30$, and $p = 0.5$ into the formula

Step 3 ：Simplify the denominator: $\sqrt{\frac{0.5 \cdot (1-0.5)}{1320}} = \sqrt{\frac{0.25}{1320}}$

Step 4 ：Calculate the square root of 5280: $\sqrt{5280} = 72.7279$

Step 5 ：Multiply $-0.20$ by $72.7279$: $-0.20 \cdot 72.7279 = -14.5456$

Step 6 ：Round to two decimal places: $-14.5456 \approx -14.55$

Step 7 ：The correct answer is $\boxed{-14.55}$