Question

# 1. The following are body mass index (BMI) scores measured in 12 patients who are free...

1. 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. 25 27 31 33 26 28 38 41 24 32 35 40

a) Calculate the 95% confidence interval estimate of the true BMI.

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.

Solution:

Part a

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

We are given

Confidence level = 95%

From given data, we have

Xbar = 31.66666667

S = 5.882691612

n = 12

df = n – 1 = 12 – 1 = 11

Critical t value = 2.2010

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 31.66666667 ± 2.2010*5.882691612/sqrt(12)

Confidence interval = 31.66666667 ± 2.2010*1.698186793

Confidence interval = 31.66666667 ± 3.7377

Lower limit = 31.66666667 - 3.7377 = 27.9290

Upper limit = 31.66666667 + 3.7377 = 35.4044

Confidence interval = (27.9290, 35.4044)

Part b

We are given

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Estimate for σ = 5.882691612

Margin of error = E = 2

Sample size formula is given as below:

n = (Z*σ/E)^2

n = (1.96*5.882691612/2)^2

n = 33.23566

Required sample size = 34