find the value of the test statistic ( z ) using ( z=\frac{hat{p}-p}{sqrt{\frac{p q}{n}}} ).
the claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include ( n = 696 ) drowning deaths of children with ( 30 % ) of them attributable to beaches.
a. ( -2.88 )
b. ( 3.05 )
c. ( -3.05 )
d. ( 2.88 )

Question

Accepted Answer

# Explanation:
## Step1: Identify the values
Given $n = 696$, $\hat{p}=0.3$, $p = 0.25$, and $q=1 - p=1 - 0.25 = 0.75$

## Step2: Substitute into the formula
$$
\begin{align*}
z&=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}\
&=\frac{0.3 - 0.25}{\sqrt{\frac{0.25\times0.75}{696}}}\
&=\frac{0.05}{\sqrt{\frac{0.1875}{696}}}\
&=\frac{0.05}{\sqrt{0.00026939655}}\
&=\frac{0.05}{0.016413}\
&\approx2.88
\end{align*}
$$

# Answer:
D. $2.88$

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Question

Explanation:

Step1: Identify the values

Step2: Substitute into the formula

Answer: