Question

1. 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) -3.05
b) -2.88
c) 3.05
d) 2.88

Explanation:

Step1: Calculate \(p\) and \(q\)

Given \(p = 0.25\), then \(q=1 - p=1 - 0.25 = 0.75\)

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

The formula for the test - statistic \(z\) for a proportion is \(z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}\)
Here, \(\hat{p}=0.30\), \(p = 0.25\), \(q = 0.75\), \(n = 696\)
First, calculate \(\sqrt{\frac{pq}{n}}=\sqrt{\frac{0.25\times0.75}{696}}=\sqrt{\frac{0.1875}{696}}\approx\sqrt{0.00027}\approx0.0164\)
Then \(z=\frac{0.30 - 0.25}{0.0164}=\frac{0.05}{0.0164}\approx3.05\)

Answer:

C. 3.05