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§9.2 Testing the Difference of Two Means
(with large independent samples)
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Assumptions for the z-test of two means:
•  The samples from each population must be independent of
one another.
•  The populations from which the samples are taken must be
normally distributed and the population standard
deviations must be know, or the sample sizes must be large
(i.e. n1≥30 and n2≥30.
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The test statistic:
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Example:
A medical researcher wishes to see whether the pulse rates of
smokers are higher than the pulse rates of non-smokers. Samples
of 100 smokers and 100 nonsmokers are selected. The results are
shown below. Can the researcher conclude at α = .05, that smokers
have higher pulse rates than nonsmokers?
H0: µ1 - µ2 = 0 H1: µ1 - µ2 > 0
Smokers
Nonsmokers
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Example
A researcher claims that students in a private school have exam
scores that are at most 8 points higher than those of students in
public schools. Random samples of 45 and 60 students from each
type of school are selected and given an exam. At α = 0.05 test the
hypothesis H0: µ1 - µ2 = 8 against H1: µ1 - µ2 > 8 Private Schools
Public schools
s1 = 12
n1 = 45
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Confidence intervals for the difference of two means.
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Example (construction of a confidence interval)
Two groups of students are given a problem-solving test, and the
results are compared. Find the 90% confidence interval of the true
difference in means. Mathematics Majors
Computer Science
Majors
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