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. 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. We will be using rules for combining independent variables that we discussed in chapter 7.

Two Sample t-test/t-interval 1. Hypotheses 1. Hypotheses H 0 : μ 1 = μ 2 H a : μ 1 > < ≠ μ 2 OR OR H 0 : μ 1 - μ 2 = 0 H a : μ 1 - μ 2 > < ≠ 0 *It is possible that μ 1 - μ 2 = something other than 0, but that is rare.* *It is possible that μ 1 - μ 2 = something other than 0, but that is rare.*

2 Sample t-test/interval 2. Conditions 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. (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. (b) Normality: Same as before, but you must check for both populations/groups.

2 sample t-test/interval 2. Conditions continued…. 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. (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. In order to verify conditions, you need to analyze how the data was collected.

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

2 proportion z interval *Normality  n 1 (p-hat 1 ), n 1 (1 - p-hat 1 ), n 2 (p-hat 2 ), and n 2 (1 - p-hat 2 ) must all be greater than 5. *Normality  n 1 (p-hat 1 ), n 1 (1 - p-hat 1 ), n 2 (p-hat 2 ), and n 2 (1 - p-hat 2 ) must all be greater than 5.

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