Question 136381: 15.28 Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic,Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why? (Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At a = .05, is the correctness of the prediction different for the two types of cola drinkers? Since it is a 2 x 2 table, try also a two-tailed two-sample z test for π1 = π2 and verify that z² is the same as your chi-square statistic.
Correct? Regular Diet Row Total
Yes....... 7..... 7..... 14
No....... 12.... 20..... 32
Total.... 19.... 27..... 46
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Ho: mu1=mu2
Ha: mu1 is not equal to mu2
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Chi-Sq:
Test statistic: Chi-Sq = 0.62768...
p-value: 0.4282
df=1
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Conclusion: Fail to reject Ho because p-value > alpha.
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2-Sample z-Test
Test statistic: z=-1.4486
p-value: 0.14746...
Conclusion: Fail to reject Ho because p-value > alpha.
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Cheers,
Stan H.
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