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Unformatted text preview: Chap 101 Chapter 10 Hypothesis Testing: Additional Topics Statistics for Business and Economics Chap 102 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 chisquare 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 103 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 104 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 105 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 106 Lowertail test: H : x y H 1 : x y < 0 Uppertail test: H : x y 0 H 1 : x y > 0 Twotail test: H : x y = 0 H 1 : x y 0 Paired Samples Decision Rules: Matched Pairs /2 /2 t t /2 t t /2 Reject H if t < t n1, Reject H if t > t n1, Reject H if t < t n1 , /2 or t > t n1 , /2 Where n s D d t d = has n  1 d.f . Chap 107 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. 20 614 M.H. 3 2 1 R.K. M.O. 4 421 d = d i n 5.67 1 n ) d (d S 2 i d = = =  4.2 Chap 108 Has the training made a difference in the number of complaints (at the = 0.01 level)? 4.2 d = 1.66 5 5.67/ 4.2 n / s D d t d = = = H : x y = 0 H 1 : x y Test Statistic: Critical Value = 4.604 d.f. = n  1 = 4 Reject /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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 Spring '11
 Peter
 Economics

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