5 test 5 test Body Mass Index In a survey of adults with dia

5 test

5 test Body Mass Index: In a survey of adults with diabetes. the average body mass index (BMI) in a sample of 1935 women was 32.5 with a standard deviation of 0.2. The BMI in a sample of 1564 men was 30.8, with a standard deviation of 0.5. Part 1 out of 2 Construct a 99.9% confidence interval for the difference in the mean BMI between women and men with diabetes. Let Mu1 denote the mean BMI for the woman and round the answers to two decimal places. A 99.9% confidence interval for the difference in the mean BMI between women and men with diabetes is

Solution

Given a=1-0.999=0.001, Z(0.0005) =3.29 (from standard normal table)

So the lower bound is

(xbar1-xbar2) -Z*sqrt(s1^2/n1+s2^2/n2)

=(32.5-30.8)-3.29*sqrt(0.2^2/1935+0.5^2/1564)

=1.66

So the upper bound is

(xbar1-xbar2) +Z*sqrt(s1^2/n1+s2^2/n2)

=(32.5-30.8)+3.29*sqrt(0.2^2/1935+0.5^2/1564)

=1.74