Question

a clinical trial tests a method designed to increase the probability of conceiving a girl in the study 504 babies were born and 252 of them were girls use the sample data to construct a 99% confidence interval estimate of the percentage of girls born based on the result does the method appear to be effective

Answer 1

We know that

• n = 504.

Then, we find the p-hat value, which is the ratio between the number of baby girls and the total number of babies born.

`p=(252)/(504)=0.5`

Now, we find the standard error.

`\begin{gathered} E=\sqrt[]{(p(1-p))/(n)}=\sqrt[]{(0.5(1-0.5))/(504)}=\sqrt[]{(0.5\cdot0.5)/(504)} \\ E\approx0.022 \end{gathered}`

Then, we use the z-score for 99% of confidence, which is 2.58. At this point, we just have to write the intervals using the information above

`p\pm z\cdot E=0.5\pm2.58\cdot0.022=0.5\pm0.057`

The limits of the interval are 0.443 and 0.557.

Hence, the confidence interval is

`\lbrack0.443;0.557\rbrack`