# The mean body mass index (BMI)

The mean body mass index (BMI) for boys age 12 is 23.6. Aninvestigator wants to test if the BMI is higher in 12-year-old boysliving in New York City. How many boys are needed to ensure that atwo-sided test of hypothesis has 80% power to detect a differencein BMI of 2 units? Assume that the standard deviation in BMI is5.7

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 testof hypothesis.

Formula:

where

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

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

That is :

and

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

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 testof hypothesis has 80% power to detect a difference in BMI of 2units.

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"

Pages (275 words)
Standard price: \$0.00
Client Reviews
4.9
Sitejabber
4.6
Trustpilot
4.8
Our Guarantees
100% Confidentiality
Information about customers is confidential and never disclosed to third parties.
Original Writing
We complete all papers from scratch. You can get a plagiarism report.
Timely Delivery
No missed deadlines – 97% of assignments are completed in time.
Money Back