Apply Your Knowledge 16.8 Confidence Level and Margin of Error. Example 16.1 (page 368) described NHANES survey data on the body mass index (BMI) of 936 young men. The mean BMI in the sample was x =27.2. We treated these data as an SRS from a Normally distributed population with standard deviation o=11.6. Give three confidence intervals for the mean BMI u in this population, using 90%, 95%, and 99% confidence. What are the margins of error for 90%, 95%, and 99% confidence? How does increasing the confidence level change the margin of error of a confidence interval when the sample size and population standard deviation remain the same?Figure 16.1 illustrates the behavior of the interval x 40.8 for the mean BMI of young men. Starting with the population, imagine taking many SRSs of 936 young men. The first sample has x =27.2, the second has x =27.4, the third has x =26.8, and so on. The sample mean varies from sample to sample, but when we use the formula x 40.8 to get an interval based on each sample, 95% of these intervals capture the unknown population mean u. Notice that we use the same margin of error, 0.8, for each interval because the sample size and standard deviation o are the same