Comparison of Two Populations: Similarities in Hypothesis Test Processes

1. Lesson 11 – R Review of Chapter 11 Comparison of Two Populations

2. Similarities in Hypothesis Test Processes

3. Putting it All Together 1 1 --- + --- n1 n2 (x1 – x2) – (μ1 – μ2 ) t0 = ------------------------------- s12 s22 ----- + ----- n1 n2 where x1 + x2 p = ------------ n1 + n2 d – μd t0 = ------------ sd /n Provided each sample size ≥ 30 or differences come from population that is normally distributed, use t-distribution with n-1 degrees of freedom and Provided np(1-p) ≥ 10 and n ≤ 0.05N for each sample, use normal distribution with p1 – p2 z0 = --------------------------------- p(1-p) proportion, p Independent What parameters are addressed in the claim? Dependent or Independent Sampling μ Dependent s or s2 Provided each sample size ≥ 30 or differences come from population that is normally distributed, use t-distribution with n-1 degrees of freedom and Provided data are normally distributed, use F-distribution with s12 F0 = ------------ s22

4. Multiple Choice Evaluations Which of the following is a characteristic of dependent (or matched-pairs) samples? • The observations from the sample are matched to the hypothesis being tested • The observations from sample 1 and sample 2 are paired with each other • The observations from sample 1 are independent of the observations from sample 2 • The mean of sample 2 depends on the mean of sample 1 Section 1

5. Multiple Choice Evaluations When we have dependent (or matched-pairs) data, then we should • Test the equality of their squares using a chi-square distribution • Test the equality of their means using proportions • Test the equality of their variances using a normal distribution • Test their differences using a student t-distribution Section 1

6. Multiple Choice Evaluations A researcher collected data from two sets of patients, both chosen at random from a large population of patients. If there is no interaction between the two groups, then this is an example of • Independent samples • Dependent samples • Stratified sampling • Descriptive statistics Section 2

7. Multiple Choice Evaluations The standard deviation for the difference of two means from independent samples involves • The standard deviation of each sample • The mean of each sample • The difference between the two means • All of the above Section 2

8. Multiple Choice Evaluations To compare two population proportions, we • Multiply the two proportions and take the square root • Subtract one proportion from the other and divide by the appropriate standard deviation • Subtract one proportion from the other and use the chi-square distribution • Divide one proportion by the other and use the normal distribution Section 3

9. Multiple Choice Evaluations If a researcher requires 100 subjects in sample 1 and 100 subjects in sample 2 to achieve a particular margin of error, then the number of subjects required to halve the margin of error is • 200 subjects in each of sample 1 and sample 2 • 200 subjects in sample 1 and 100 subjects in sample 2 • 50 subjects in each of sample 1 and sample 2 • 400 subjects in each of sample 1 and sample 2 Section 3

10. Multiple Choice Evaluations To test for the equality of two population standard deviations, we use for the test statistic • The difference between the two standard deviations • The ratio of the two standard deviations • The product of the two standard deviations • The ratio of the squares of the two standard deviations Section 4

11. Multiple Choice Evaluations To test for the equality of two population standard deviations, we use • The normal distribution • The beta distribution • The F distribution • The chi-square distribution Section 4

12. Summary and Homework • Summary • We can test whether sample data from two different samples supports a hypothesis claim about a population mean, proportion, or standard deviation • For two population means, there are two cases • Dependent (or matched-pair) samples • Independent samples • All of these tests follow very similar processes as hypothesis tests on one sample • Homework • pg 625 – 628; 1, 4, 6, 7, 10, 11, 14, 15, 21

13. Homework Answers • 4) Dependent • 6) a) 2.06 b) 0.49 • 10) a) Reject H0 b) [-12.44, 0.04] c) Reject H0 • 14) a) H0: p1 = p2 H1: p1 < p2 b) z0 = -0.62 c) zc = -1.645 d) p = 0.2611 FTR H0