Given that the claim is that the proportion of drowning deaths of children attributable
to beaches is more than 0.25 [tex](p\ \textgreater \ 0.25)[/tex], and the sample statistics include n = 575
drowning deaths of children with 30 percent [tex](\hat{p}=0.3)[/tex] of them attributable to
beaches.
The value of the test statistic z is given by
[tex]z= \frac{\hat{p}-p}{\sqrt{ \frac{p(1-p)}{n} }} \\ \\ =\frac{0.3-0.25}{\sqrt{ \frac{0.25(1-0.25)}{575} }} \\ \\ = \frac{0.05}{\sqrt{\frac{0.25(0.75)}{575}}} = \frac{0.05}{\sqrt{\frac{0.1875}{575}}} \\ \\ = \frac{0.05}{\sqrt{0.0003261}} = \frac{0.05}{0.0181} =2.769[/tex]
Therefore, the value of the test statistics is 2.769
