Question

An article presents results of a survey of adults with diabetes. The average body mass index (BMI) in a sample of 15 men was 30.4, with a standard deviation of 0.6. The average BMI in a sample of 19 women was 31.1 with a standard deviation of 0.2. Assuming BMI is normally distributed, find a 95% confidence bound for the difference in mean BMI between men and women with diabetes. Be sure to interpret the interval in context.

Answer 1

We need to construct the 95% confidence interval for the difference between the population means μ1​−μ2​, for the case that the population standard deviations are not known. The following information has been provided about each of the samples:

Based on the information provided, we assume that the population variances are equal, so then the number of degrees of freedom are

The critical value for α=0.05 and df=32 degrees of freedom is

Therefore, based on the data provided, the 95% confidence interval for the difference between the population means μ1​−μ2​ is −0.998<μ1​−μ2​<−0.402, which indicates that we are 95% confident that the true difference between population means is contained by the interval (−0.998,−0.402).

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