Question

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 556 babies were​ born, and 278 of them were girls.

Use the sample data to construct a 99​% confidence interval estimate of the percentage of girls born.

Answer 1

To solve this problem, we make use of the z statistic. The formula for the confidence interval can be calculated using the formula:

Confidence Interval = p ± MOE

where,

p is the portion of girls = 278 / 556 = 0.5

MOE is the margin of error

We calculate the margin of error using the formula:

MOE = z * sqrt[p (1 – p) / n]

From the standard distribution tables, the value of z at 99% confidence is:

z = 2.58

Therefore the MOE is:

MOE = 2.58 * sqrt[0.5 (0.5) / 556]

MOE = 0.055

Therefore the confidence interval is:

Confidence Interval = 0.5 ± 0.055

Confidence Interval = 0.445, 0.555

0.445<p<0.555