Question

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 390 babies were​ born, and 312 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

Answer:Yes

Step-by-step explanation:

Given

n=390 x=312

$\hat{p}=\frac{312}{390}=0.8$

Confidence level=99 %

$Z_{\frac{\alpha }{2}}=2.575$

Standard error(S.E.)=$\sqrt{\frac{\hat{p}\left ( 1-\hat{p}\right )}{n}}$

S.E.=$\sqrt{\frac{0.8\times 0.2}{390}}$

S.E.=0.0202

Confidence interval

$p\pm \left [ z_{\frac{\alpha }{2}}\cdot S.E.\right ]$

$0.8 \pm 0.0521$

$\left ( 0.7479,0.8521 \right )$

Since 0.5 does not lie in interval therefore method appear to be effective