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: At

Question 131000This question is from textbook Applied Statistics in Business and Economics
: 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?
Yes got it right - 7, 7, 14
no got it wrong - 12, 20, 32
total - 19, 27, 46 This question is from textbook Applied Statistics in Business and Economics

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?
Yes got it right - 7, 7, 14
no got it wrong - 12, 20, 32
total - 19, 27, 46
-----------------
Chi-Sq Test:
Ho: the columns are homogeneous
Ha; the columns are not homogeneous
Using a TI-calculator Chi-Sq Test I get:
Test statistic: Chi-Sq = 0.62768....
p-value = 0.428..
--------
Conclusion: Reject Ho;
The columns are not homogeneous
=======================================
Two-tailed sample z test:
Ho: mu1 = mu2
Ha: mu1 is not equal to mu2
Critical value for 2-tailed test and alpha=5%: +-1.96
--------
x1-bar = 19/2= 9.5
x2-bar = 27/2= 13.5
sigma1^2 =7.77817^2 = 60.5
n1=19
sigma2^2 =9.1924^2=84.5
n2=27
---------------
z(9.5-13.5)/sqrt[(60.5/19) + (84.5)/27] = -1.59
p-value = 2P(-10 < z <-1.59) = 0.1118...
--------
Conclusion: Since p-value > alpha, Fail to Reject Ho.
The columns are homogeneous.
-----------------------------
As you see, the test results are not the same.
I'll leave the discussion of the final questions to you.
-----------------------------
Cheers,
Stan H.

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