chap10 - Chap 10-1 Chapter 10 Hypothesis Testing Additional...

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Unformatted text preview: Chap 10-1 Chapter 10 Hypothesis Testing: Additional Topics Statistics for Business and Economics Chap 10-2 Chapter Goals After completing this chapter, you should be able to: Test hypotheses for the difference between two population means Two means, matched pairs Independent populations, population variances known Independent populations, population variances unknown but equal Complete a hypothesis test for the difference between two proportions (large samples) Use the chi-square distribution for tests of the variance of a normal distribution Use the F table to find critical F values Complete an F test for the equality of two variances Chap 10-3 Two Sample Tests Two Sample Tests Population Means, Independent Samples Population Means, Matched Pairs Population Variances Group 1 vs. independent Group 2 Same group before vs. after treatment Variance 1 vs. Variance 2 Examples: Population Proportions Proportion 1 vs. Proportion 2 (Note similarities to Chapter 9) Chap 10-4 Matched Pairs Tests Means of 2 Related Populations Paired or matched samples Repeated measures (before/after) Use difference between paired values: Assumptions: Both Populations Are Normally Distributed Matched Pairs d i = x i- y i Chap 10-5 The test statistic for the mean difference is a t value, with n – 1 degrees of freedom : n s D d t d- = Test Statistic: Matched Pairs Where D = hypothesized mean difference s d = sample standard dev. of differences n = the sample size (number of pairs) Matched Pairs Chap 10-6 Lower-tail test: H : μ x – μ y ≥ H 1 : μ x – μ y < 0 Upper-tail test: H : μ x – μ y ≤ 0 H 1 : μ x – μ y > 0 Two-tail test: H : μ x – μ y = 0 H 1 : μ x – μ y ≠ 0 Paired Samples Decision Rules: Matched Pairs α α /2 α /2 α-t α-t α /2 t α t α /2 Reject H if t < -t n-1, α Reject H if t > t n-1, α Reject H if t < -t n-1 , α/2 or t > t n-1 , α/2 Where n s D d t d- = has n - 1 d.f . Chap 10-7 Assume you send your salespeople to a “customer service” training workshop. Has the training made a difference in the number of complaints? You collect the following data: Matched Pairs Example Number of Complaints : (2) - (1) Salesperson Before (1) After (2) Difference, d i C.B. 6 4- 2 T.F. 20 6-14 M.H. 3 2- 1 R.K. M.O. 4- 4-21 d = Σ d i n 5.67 1 n ) d (d S 2 i d =-- = ∑ = - 4.2 Chap 10-8 Has the training made a difference in the number of complaints (at the α = 0.01 level)?- 4.2 d = 1.66 5 5.67/ 4.2 n / s D d t d- =-- =- = H : μ x – μ y = 0 H 1 : μ x – μ y ≠ Test Statistic: Critical Value = ± 4.604 d.f. = n - 1 = 4 Reject α /2- 4.604 4.604 Decision: Do not reject H (t stat is not in the reject region) Conclusion: There is not a significant change in the number of complaints....
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chap10 - Chap 10-1 Chapter 10 Hypothesis Testing Additional...

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