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AP Statistics Chapter 13 Notes
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.
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.*
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.
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.
2-sample t-test/t-interval • 3. Calculations • 4. Conclusion
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.
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