SOLUTION: 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: A

Question 178521: 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. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers?
--
Run a Chi-Sq test on the 2x2 set of data.
Test Stat = 0.6277.. ; p-value = 0.426..; df = (2-1)(2-1)=1
Fail to Reject Ho; row and column factors are independent
------------------------------------------
Could you identify your favorite brand in this kind of test?
No, Yes and No are independent of Coke type; opinion is random.
-----------------------------------------------------------------------
Since it is a 2 � 2 table, try also a two-tailed two-sample z test for π1 = π2
Ho: p1-p2 = 0
Ha: p1-p2 is not equal to 0
Test Stat: z((7/19)-(7/27)) = 0.7933..
p-value = 0.43
Conclusion: Fail to reject Ho; the proportions are equal
---------------------------------------------------------------
(see Chapter 10) and verify that z^2 is the same as your chi-square statistic.
z^2 = 0.7933^2= 0.6277 ; Chi-Sq = 0.6277...
-------------------------------
Which test do you prefer? Why?
Chi-Sq: It's easier to run on the calculator.
==============
Cheers,
Stan H.
P.S. This answer is several days late. Was it any help?
=============================================================
-----------------------------
(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

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