{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chapter11

# chapter11 - Chapter 11 Inferences on Two Samples 11.1...

This preview shows pages 1–3. Sign up to view the full content.

561 Chapter 11 Inferences on Two Samples 11.1 Inferences about Two Means: Dependent Samples 1. independent 2. dependent 3. Since the researcher claims the mean of population 1, 1 μ , is less than the mean of population 2, 2 μ , in matched pair data, the difference 1 2 μ μ should be negative. Thus, define 1 : 0 d H μ < with i i i d X Y = . 4. To test a claim regarding the differences of two means with dependent sampling, (1) the sample must be obtained using simple random sampling; (2) the sample must be matched pairs; and (3) the differences must either be normally distributed with no outliers or the sample size must be large (i.e., 30 n ). 5. Since the members of the two samples are married to each other, the sampling is dependent. 6. Because the 100 subjects are randomly allocated to one of two groups, the sampling is independent. 7. Because the 80 students are randomly allocated to one of two groups, the sampling is independent. 8. Because the samples are obtained by giving different treatments to the same subjects, the sampling is dependent. 9. Because the two sets of twins are chosen at random, the sampling is independent. 10. Because the 30 subplots are randomly allocated to one of two groups, the sampling is independent. 11. (a) 7.6 7.6 7.4 5.7 8.3 6.6 5.6 8.1 6.6 10.7 9.4 7.8 9.0 8.5 0.5 1.0 3.3 3.7 0.5 2.4 2.9 i i i i i X Y d X Y = Observation 1 2 3 4 5 6 7 (b) Using technology, 1.614 d ≈ − and 1.915 d s . (c) The hypotheses are 0 : 0 d H μ = versus 1 : 0 d H μ < . The level of significance is 0.05 α = . The test statistic is 0 1.614 2.230 / 1.915/ 7 d d t s n = = ≈ − . Classical approach : Since this is a left-tailed test with 6 degrees of freedom, the critical value is 0.05 1.943 t = − . Since the test statistic 0 2.230 t ≈ − is less than the critical value 0.05 1.943 t = − (i.e., since the test statistic fall within the critical region), we reject 0 H .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document