7 Comparison of Population Means
If each element of a data set may lie at only a few isolated points, we have a
discreteorcategorical data set; examples include gender, race, and some sort of
artificial grading used as outcomes. If each element of a data set may lie any-
where on the numerical scale, we have acontinuous data set; examples include
blood pressure, cholesterol level, and time to a certain event. In Chapter 6 we
dealt with the analysis of categorical data, such as comparing two proportions.
In this chapter we focus on continuous measurements, especially comparisons
of population means. We follow the same layout, starting with the simplest
case, the one-sample problem.
7.1 ONE-SAMPLE PROBLEM WITH CONTINUOUS DATA
In this type of problem we have a sample of continuous measurements of sizen
and we consider the null hypothesis
H 0 :m¼m 0wherem 0 is a fixed and known number. It is often a standardized or referenced
figure; for example, the average blood pressure of men in a certain age group
(this figure may come from a sample itself, but the referenced sample is often
large enough so as to produce negligible sampling error inm 0 ). Or, we could be
concerned with a question such as: Is the average birth weight for boys for this
particular sub-population below normal averagem 0 : say, 7.5 lb? In Exercise 7.1,
we try to decide whether air quality on a certain given day in a particular city
exceeds regulated limitm 0 set by a federal agency.
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