review-on-testing

15 ha h0 fails to hold 2 k i1 brand 1 2 3 4 f i

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Unformatted text preview: 256 144 400 Problem 3 - continued H0: preference independent of age group Ha: preference is not independent of age group \ Preference Age Bad News First Good News First 21-34 83 (64) 17 (36) 35-44 50 (64) 50 (36) 45-54 53 (64) 47 (36) >55 70 (64) 30 (36) (observed − expected )2 χ2 = ∑ expected all cells (83 − 64)2 (50 − 64)2 (30 − 36 )2 = + + ... + 64 64 36 = 5.641 + 3.063 + ... + 1.000 = 30.99 df = ( 4 − 1)(2 − 1) = 3 Critical − value = 11.345 Extremely strong evidence against the null hypothesis: reject null Problem 4 Microwave oven wholesaler wishes to compare consumer preferences in Milwaukee with the historical market shares in Cleveland. If the consumer preferences in Milwaukee are substantially different, the wholesaler will consider changing its policies for stocking ovens. The wholesaler examines a random sample of 400 Milwaukee consumers. Test the hypothesis at 5% level. Brand Cleveland Market Share Milwaukee Frequency 1 20% 102 2 35% 121 3 30% 120 4 15% 57 Problem 4- continued H0: p1 = 0.20, p2 = 0.35, p3 = 0.30, p4 = 0.15 Ha: H0 fails to hold 2 k χ =∑ i=1 Brand 1 2 3 4 (f i − Ei )2 Cleveland Milwaukee Expected Market Share Frequency Frequency 20% 102 80 35% 121 140 30% 120 120 15% 57 60 Ei (102 − 80)2 (121 − 140)2 (120 − 120)2 (57 − 60)2 = + + + 80 140 120 60 = 6.0500 + 2.5786 + 0.0000 + 0.1500 = 8.7786 χ 2 = 8.7786 Critical − value = χ.2 5 0 2 = 7.815 p − value = P( χ > 8.7786) = 0.0324 ( software) ChiSq i 6.0500 2.5786 0.0000 0.1500 8.7786 df = (4- 1) = 3 REJECT NULL Problem 5 Test at 1% level if client satisfaction depend on investment fund type? Client Satis...
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