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

Explanation:

Given

n=390 x=312

`\hat{p}=(312)/(390)=0.8`

Confidence level=99 %

`Z_{(\alpha )/(2)}=2.575`

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

S.E.=
`\sqrt{(0.8* 0.2)/(390)}`

S.E.=0.0202

Confidence interval

`p\pm \left [ z_{(\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