Question

find the value of the test statistic z using ( z = \frac{hat{p} - p}{sqrt{\frac{pq}{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 = 616 ) drowning deaths of children with 30% of them attributable to beaches.
a. -3.06
b. 3.06
c. 2.86
d. -2.86

Explanation:

Step1: Identify the values

Given \(n = 668\), \(\hat{p}=0.30\), \(p = 0.25\), and \(q=1 - p=1 - 0.25 = 0.75\)

Step2: Calculate the test - statistic \(z\)

Use the formula \(z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}\)
Substitute the values:

$$
LATEXBLOCK0
$$

Answer:

B. \(3.06\)