SOLUTION: Can someone please help me with this Chi-square question? Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke

Question 145173: Can someone please help me with this Chi-square question?

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.)
Cola
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. 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.)
-------------
Cola
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
--------------------------------
Ho: Results are the same for Coke and Pepsi drinkers
Ha: Results are different.
------------
I ran a Chi-Sq. Test on the 2 x 2 data and got the following results:
test statistic: Chi-Sq = 0.62768..
p-value: 0.4282...
Conclusion: Since the p-value is greater than 5%, Fail to reject Ho.
===================
Ho: p(coke yes)-p(pepsi yes) = 0
Ha: p(coke yes)-p(pepsi yes) is not zero
--------------------
I ran a two proportion zTest and got the following results:
test statistic: z = 0.792268...
p-value = 0.428207...
Conclusion: Fail to reject Ho.
--------------
z^2 = Chi-Sq test statistic ?
0.792268^2 = 0.627688
===============
Cheers,
Stan H.

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