Question

A clinical trial tests a method designed to increase probability of conceiving a girl. In the study 350 babies were born, and 280 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percetage of girls born. Based on the result, does the method appear to be effective

Answer 1

Recall that for a 99% confidence interval, the \(Z_{\alpha/2}\) value is 2.575

The confidence interval for a proportion (or percentage") has the form:
\[\large\left(\hat{p}-2.575\sqrt\frac{\hat{p}(1-\hat{p})}{{n}},\hat{p}+2.575\sqrt\frac{\hat{p}(1-\hat{p})}{{n}}\right) \]

Here, \(n=350\) and \(\large \hat{p}=\frac{280}{350}\), so just plug those values into the 'formula' above!