Problem

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 \(\boxed{-14.55}\)

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