The following are body mass index (BMI) scores measured in 12 patients who are f

Question

The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared.
A). Generate a 95% confidence interval estimate of the true BMI. 25 27 31 33 26 28 38 41 24 32 35 40.

B). How many subjects would be needed to ensure that a 95% confidence interval estimate of BMI had a margin of error not exceeding 2 units?

Please show your work with answer.

Explanation / Answer

1. Given n=12, xbar=31.67, s= 5.88 (based on the data)
a=0.05, |t(0.025,df=n-1=11)|=2.2 (check student t table)

So 95% CI is
xbar±t*s/n

--> 31.67±2.2*5.88/sqrt(12)

--> (27.9357, 35.4043)

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