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.

$p=\frac{252}{504}=0.5$

Now, we find the standard error.

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

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

$\lbrack0.443;0.557\rbrack$