Question

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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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.

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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