A researcher measured BMI in 12 patients who are free of diabetes and participating in a study of risk factors for obesity and found a mean BMI of 31.7 with a standard deviation of 5.9. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. Generate a two-sided 95% confidence interval estimate of the true BMI. You MUST show your work to receive full credit.

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Asked Oct 15, 2019
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A researcher measured BMI in 12 patients who are free of diabetes and participating in a study of risk factors for obesity and found a mean BMI of 31.7 with a standard deviation of 5.9. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. Generate a two-sided 95% confidence interval estimate of the true BMI. You MUST show your work to receive full credit.

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Expert Answer

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Step 1

Confidence interval when population standard deviation is not known:

The formula of confidence interval for the population mean when population standard deviation is not given is as follows.

Confidence interval = x f2 Tn
< fu<| X +[a2 _n
where, Sample mean
Margin of error
= Lower limit of the mean
= Upper limit of the mean
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Confidence interval = x f2 Tn < fu<| X +[a2 _n where, Sample mean Margin of error = Lower limit of the mean = Upper limit of the mean

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Step 2

Computing the 95% confidence interval for population mean:

Here, the sample mean (x-bar) is 31.7.

The sample standard deviation (s) is 5.9.

The confidence level is 0.95.

Thus, the level of significance, α is 0.05 (= 1 – 0.95).

The degrees of freedom (n − 1) is 11 (=12 − 1).

For 95% confidence interval, the cri...

-20)-20)
5.9
31.7-2.201x
V12
5.9
< U < 31.7 2.201x
v12
(31.7-3.75)< u(31.7+3.75)
27.95 <u<35.45
help_outline

Image Transcriptionclose

-20)-20) 5.9 31.7-2.201x V12 5.9 < U < 31.7 2.201x v12 (31.7-3.75)< u(31.7+3.75) 27.95 <u<35.45

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