Question 132971: Please help. Found the question but the calculations were not available. Thank you in advance. 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 alpha=.05, is the correctness of the prediction different for the two types of cola drinker? Could you identify your favorite brand in this kind of test? Since it is a 2x2 table, try also a two taled two sample z test for п1= п2 and verify that z2 is the same as your chi-square statistic. Which test do you prefer? Why?
Show how the degrees of freedom are calculated, find the critical value of chi-square, and interpret the p-value. Is the conclusion sensitive to the level of significance chosen?
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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Correct?............ Reg 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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Research question: at alpha=.05,
Is the correctness of the prediction different for the two types of cola drinker?
Ho: They are the same
Ha: They are different
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un a Chi-Sq. Test on the 2X2 data:
Reg Cola: 7....12
DietCola: 7....20
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Test statistic: Chi-Sq = 0.62768...
p-value = 0.428207...
Show how the degrees of freedom are calculated,
df= (# of rows -1)(# of columns) = 1*1 = 1
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Find the critical value of chi-square for alpha = 5% and df=1,
Left margin = 0.001; Right margin is 7.879
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Interpret the p-value.
At least 43.8% of test results could provide stronger evidence for
rejecting Ho.
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Since p-value is greater then alpha = 5%, Fail to Reject Ho.
Conclusion: Correctness of the predictions of RegCola and DietCola drinkers is not different.
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Could you identify your favorite brand in this kind of test?
Probably not since this test group was wrong in their identification
32 out of 46 times.
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Since it is a 2x2 table, try also a two tailed two sample z test for p1= p2 and verify that z2 is the same as your chi-square statistic.
Ho: p1-p2=0
Ha: p1-p2 is not 0
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Critical Value for 2-tail 2-proportion z test with alpha=5%: z = +/-1.96
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If data is pooled p-bar = (x1+x2)/(n1+n2) =14/46 = 0.304
Test statistic:
z(7/19 - 7/27) = 0.10916/sqrt[(0.304*0.696/19) + (0.304*0.696/27)]
= 0.10916/sqrt(0.01897) = 0.015056...
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Conclusion: Since the test statistic is between -1.96 and +1.96, Fail to Reject Ho.
The proportions are the same.
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Show how the degrees of freedom are calculated,
df= (# of rows -1)(# of columns) = 1*1 = 1
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Find the critical value of chi-square,
Left margin = 0.001; Right margin is 7.879
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p-value for the test statistic = 2P(z > 0.015056...) = 98.8%
Interpret the p-value: 98.8% of the test results could have
provided stronger evidence to reject Ho..
Is the conclusion sensitive to the level of significance chosen?
Not when the p-value is as large as 98.9%
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Which test do you prefer? Why?
The Chi-Sq is much easier to run and interpret.
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Cheers,
Stan H.
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