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§9.2 Testing the Difference of Two Means

(with large independent samples)

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

Nonsmokers Smokers

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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

n1 = 45

s1 = 12

Public schools Private Schools

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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.

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