Question 183156: Hi,
Can you please help me solve for this, Doane−Seward: Applied Statistics in Business and Economics, ch. 15:
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
(This format is cramming the numbers together to make it easier to read - Correct: Yes, got it right, Regular Cola: 7, Diet Cola: 7, Row Total: 14.)
Thank you
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 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?
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Ho: row and column factors are independent
Ha: they are dependent
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I ran a Chi-Sq. test using a TI-83 on the 2x2 data array and got
Test Statistic: Chi-Sq. = 0.6277
p-value = 0.42821
df = (2-1)(2-1)
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Conclusion: Since p-value is greater than alpha = 5%, Fail to reject Ho.
The row and column factors are statistically independent: yes and no
results for the different drinkers are not statistically different.
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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)
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Ho: p1-p2 = 0
Ha: p1 is not equal to p2
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p1-hat = 7/14 ; p2-hat = 12/32
I ran a 2-Proportion z-Test on the data of got:
Test statistic = z((7/14)-(12/32)) = 0.79226
p-value = 0.41304
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Comclusion: Since p-value is greater than 5%, Fail to reject Ho
The proportions are equal
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Verify that z^2 is the same as your chi-square
(0.79226)^2 = 0.62768
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Which test do you prefer? Why?
The Chi-Sq is faster to run using a calculator.
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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