MATH 2311Section 8.3

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Comparing Two MeansTwo – sample t – tests compare the responses to two treatments or characteristics of two populations. There is a separate sample from each treatment or population. These tests are quite different than the matched pairs t – test discussed in section 8.1.How can we tell the difference between dependent and independent populations/samples?

The null and alternate hypotheses would be:

And the assumptions for a two-sample t – test are:

Two-Sample t-test statistic:

Example:The president of an all-female school stated in an interview that she was sure that the students at her school studied more, on average, than the students at a neighboring all-male school. The president of the all-male school responded that he thought the mean study time for each student body was undoubtedly about the same and suggested that a study be undertaken to clear up the controversy.Accordingly, independent samples were taken at the two schools with the following results:Determine, at the 2% level of significance, if there is a significant difference between the mean studying times of the students in the two schools based on these samples.

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