a researcher measured BMI in 12 patients who are free of diabetes in participating in the study of risk factors for obesity and found a mean BMI of 31.7 with a standard deviation of 5.9 body Mass is measured as a ratio of weight in kilograms to height in meters squared generate a two-sided 95% confidence interval estimate of the true BMI

Question
Asked Oct 21, 2019

a researcher measured BMI in 12 patients who are free of diabetes in participating in the study of risk factors for obesity and found a mean BMI of 31.7 with a standard deviation of 5.9 body Mass is measured as a ratio of weight in kilograms to height in meters squared generate a two-sided 95% confidence interval estimate of the true BMI

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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.

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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 critical ...

5.9
<u <31.7 2.201 x
5.9
31.7- 2.201 x
V12
=> 27.95 < u < 35.45
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5.9 <u <31.7 2.201 x 5.9 31.7- 2.201 x V12 => 27.95 < u < 35.45

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