Question

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 = 575 drowning deaths of children with 30 percent of them attributable to beaches.. find the value of the test statistic z using

Answer 1

Given that the claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25
`(p\ \textgreater \ 0.25)`, and the sample statistics include n = 575 drowning deaths of children with 30 percent
`(\hat{p}=0.3)` of them attributable to beaches.

The value of the test statistic z is given by


`z= \frac{\hat{p}-p}{\sqrt{ (p(1-p))/(n) }} \\ \\ =\frac{0.3-0.25}{\sqrt{ (0.25(1-0.25))/(575) }} \\ \\ = \frac{0.05}{\sqrt{(0.25(0.75))/(575)}} = \frac{0.05}{\sqrt{(0.1875)/(575)}} \\ \\ = (0.05)/(√(0.0003261)) = (0.05)/(0.0181) =2.769`

Therefore, the value of the test statistics is 2.769