Question

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.

Answer #1

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

The following are body mass index (BMI) scores measured in 12
patients who are free of diabetes and are 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. Generate
a 95% confidence interval estimate of the true BMI.
25 27 31
33 26 28
38 41 24 32
35 40

The following are body mass index (BMI) scores measured in 9
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
What is the standard deviation of BMI? You MUST show your work to
receive full credit.

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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. Using the
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25 27 31 33 26...

Suppose we want to do a study on the body mass index
(BMI) on 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.
1. How many participants would be needed to ensure that a 95%
confidence interval estimate of BMI had a margin of error not
exceeding 2 units? Assume that the standard deviation of BMI...

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

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23.6 kg/m2. 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 kg/m2? Assume
that the standard deviation in BMI is 5.7 kg/m2.
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Your body mass index (BMI) is your weight in kilograms divided
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Give your answer as a whole number.
Fill in the blank:

The body mass index (BMI) for a sample of men and a sample of
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23.8
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