SOLUTION: Thank you for all your help with this course. But my problem for this week that I am stuck on is: Can people really identify their favorite brand of cola? Volunteers tasted Coca

Question 135248: Thank you for all your help with this course. But my problem for this week that I am stuck on is:
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. At alpha = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favor brand in this kind of test? Since it is a 2 x 2 table, try also a two-tailed two-sample z tet for pi1=p12 and verify z squared is the same as your chi-square statistic. Which test do you prefer? Why?

Corect? 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
I saw this problem posted but could not find the answer. Thank you Thank you! You guys are wonderful!
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 z� 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
-----------------------------
Ho: mu1=mu2
Ha: mu1 is not equal to mu2
-------------
Chi-Sq:
Test statistic: Chi-Sq = 0.62768...
p-value: 0.4282
df=1
---------
Conclusion: Fail to reject Ho because p-value > alpha.
-------------------------------------
2-Sample z-Test
Test statistic: z=-1.4486
p-value: 0.14746...
Conclusion: Fail to reject Ho because p-value > alpha.
===================================
Cheers,
Stan H.

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