Question 149621: 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.)
Correct? Regular Cola Diet Cola Row Total
Yes, got it right 7 7 14
No, got it wrong 12 20 32
Col Total 19 27 46
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.
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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?
Chi-Square Test:
Ho: Cola type and quessing results are homogeneous (the same for both Colas)
Ha: Results are not homogeneous
Ran a Chi-Square on the 2 x 2 with the following results:
Test statistic: 0.62768...
p-value: 0.428...
Conclusion: Since the p-value is greater than 5%, fail to reject Ho.
Results are the same for both solas.
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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 z^2 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.)
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Ran a 2-sample z-Test:
Ho: u1=u2
Ha: u1 is not equal to u2
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test statistic: z = -0.72428596...
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Does z^2 = the Chi-Sq
(-0.72428596..)^2 ? 0.62768...
Not quite.
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Cheers,
Stan H.
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Correct?........... Regular Cola Diet Cola Row Total
Yes, got it right...... 7............ 7...... 14
No, got it wrong....... 12.......... 20...... 32
Col Total.............. 19.......... 27...... 46
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