Question

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 400 babies were​ born, and 320 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 < ?

​(Round to three decimal places as​ needed.)

Does the method appear to be​ effective?

No​, the proportion of girls is not significantly different from 0.5.

or

Yes​, the proportion of girls is significantly different from 0.5.

Answer 1

Solution :

Given that,

n = 400

x = 320

Point estimate = sample proportion = = x / n = 0.8

1 - = 0.2

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (((0.8*0.2) / 400)

= 0.052

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.8 - 0.052 < p < 0.8 + 0.052

0.748 < p < 0.852

No​, the proportion of girls is not significantly different from 0.5.