Question

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 606 babies were​ born, and 303 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?

____ < p < _____

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 303 / 606 = 0.500

1 - = 1 - 0.500 = 0.5

Z/2 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 * (((0.500 * 0.5) / 606)

Margin of error = E = 0.052

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.500 - 0.052 < p < 0.500 + 0.052

0.448 < p < 0.552

The 99% confidence interval for the population proportion p is : 0.448 , 0.552