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

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