## ABSTRACT

In our study of confidence intervals, we encountered the distribution of serum cholesterol levels for the population of males in the United States who are hypertensive and who smoke. This distribution is approximately normal with an unknown mean μ. However, we do know that the mean serum cholesterol level for the general population of all 20- to 74-year-old males is 211 mg/100 ml [1]. Therefore, we might wonder whether the mean cholesterol level of the subpopulation of men who are hypertensive smokers is 211 mg/100 ml as well. If we select a random sample of 25 men from this group and their mean serum cholesterol level is https://www.w3.org/1998/Math/MathML"> x ¯ = 220 m g / 100 $\bar{x} = 220mg/100$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489624/3356e2ed-5dc1-4457-a0c6-203608f5aa7a/content/inline-math10_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ml, is this sample mean compatible with a hypothesized mean of 211 mg/100 ml? We know that some amount of sampling variability is to be expected. What if the sample mean is 230 mg/100 ml, or 250 mg/100 ml? How far from 211 must https://www.w3.org/1998/Math/MathML"> x ¯ $\bar{x}$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489624/3356e2ed-5dc1-4457-a0c6-203608f5aa7a/content/inline-math10_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> be before we can conclude that μ is really equal to some other value?