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Two-sample Problems in AP Statistics

Learn how to compare the responses of two treatments or the characteristics of two populations using rules for combining independent variables. Explore the conditions and calculations necessary for a two-sample t-test/interval and two-proportion z-test/interval.

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Two-sample Problems in AP Statistics

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  1. AP Statistics Chapter 13 Notes

  2. Two-sample problems • The goal is to compare the responses of two treatments given to randomly assigned groups, or to compare the characteristics of two populations. • We will be using rules for combining independent variables that we discussed in chapter 7.

  3. Two Sample t-test/t-interval • 1. Hypotheses • H0: μ1 = μ2 Ha: μ1 > < ≠ μ2 • OR • H0: μ1 - μ2 = 0 Ha: μ1 - μ2 > < ≠ 0 • *It is possible that μ1 - μ2 = something other than 0, but that is rare.*

  4. 2 Sample t-test/interval • 2. Conditions • (a) Randomness (SRS). If you are comparing two populations, then you must have two separate SRS’s. If you are doing an experiment, the subjects must be randomly assigned to groups. • (b) Normality: Same as before, but you must check for both populations/groups.

  5. 2 sample t-test/interval • 2. Conditions continued…. • (c) Independence: The samples must have no influence on each other. If you are working with two separate populations, then you can apply the N > 10n rule. • In order to verify conditions, you need to analyze how the data was collected.

  6. 2-sample t-test/t-interval • 3. Calculations • 4. Conclusion

  7. 2 proportion z interval • *Normality n1(p-hat1), n1(1 - p-hat1), n2(p-hat2), and n2(1 - p-hat2) must all be greater than 5.

  8. 2 proportion z test • What will the hypotheses look like? • is the combined sample proportion • =count of successes in both samples combined / count of individuals in both samples combined

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