328 CHAPTER 10 STATISTICAL INFERENCE FOR TWO SAMPLES- Test hypotheses and construct confidence intervals on the ratio of the variances or standard
deviations of two normal distributions - Test hypotheses and construct confidence intervals on the difference in two population proportions
- Use the P-value approach for making decisions in hypotheses tests
- Compute power, type II error probability, and make sample size decisions for two-sample tests on
means, variances, and proportions - Explain and use the relationship between confidence intervals and hypothesis tests
CD MATERIAL - Use the Fisher-Irwin test to compare two population proportions when the normal approxima-
tion to the binomial distribution does not apply
Answers for many odd numbered exercises are at the end of the book. Answers to exercises whose
numbers are surrounded by a box can be accessed in the e-Text by clicking on the box. Complete
worked solutions to certain exercises are also available in the e-Text. These are indicated in the
Answers to Selected Exercises section by a box around the exercise number. Exercises are also
available for some of the text sections that appear on CD only. These exercises may be found within
the e-Text immediately following the section they accompany.10-1 INTRODUCTIONThe previous chapter presented hypothesis tests and confidence intervals for a single popula-
tion parameter (the mean , the variance ^2 , or a proportion p). This chapter extends those
results to the case of two independent populations.
The general situation is shown in Fig. 10-1. Population 1 has mean and variance ,
while population 2 has mean and variance. Inferences will be based on two random
samples of sizes n1 and n2, respectively. That is, X11, X12, p , is a random sample of n1
observations from population 1, and X21, X22, p , is a random sample of n2 observations
from population 2. Most of the practical applications of the procedures in this chapter arise in
the context of simple comparative experiments in which the objective is to study the differ-
ence in the parameters of the two populations.10-2 INFERENCE FOR A DIFFERENCE IN MEANS OF TWO
NORMAL DISTRIBUTIONS, VARIANCES KNOWNIn this section we consider statistical inferences on the difference in means of two
normal distributions, where the variances and are known. The assumptions for this sec-
tion are summarized as follows. 21 (^22)
1 2
X 2 n 2
X 1 n 1
2 (^22)
1 (^21)
Figure 10-1Tw o
independent popula-
tions.
1 2
Population 1 Population 2
Sample 1:
x 11 , x 12 ,..., x 1 n 1
Sample 2:
x 21 , x 22 , ..., x 2 n 2
12 22
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