Question

The mean body mass index (BMI) for boys age 12 is 23.6. An investigator wants to test if the BMI is higher in 12-year-old boys living in New York City. How many boys are needed to ensure that a two-sided test of hypothesis has 80% power to detect a difference in BMI of 2 units? Assume that the standard deviation in BMI is 5.7

Answer 1

Solution:

Given:

Power of the test =

difference in BMI = 2 units

the standard deviation in BMI = 5.7

Since level of significance is not given , we assume

We have to find sample size( Number of boys) for two-sided test of hypothesis.

Formula:

where

So we need to look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is :

and

Look in z table for area = 0.8000 or its closest area and find z value;

Area 0.7995 is closest to 0.8000

and it corresponds to 0.8 and 0.04

thus z = 0.84

Thus we get:

Thus 64 boys are needed to ensure that a two-sided test of hypothesis has 80% power to detect a difference in BMI of 2 units.