According to a recent marketing campaign, 120120 drinkers of either Diet Coke or

Question

According to a recent marketing campaign, 120120 drinkers of either Diet Coke or Diet Pepsi participated in a blind taste test to see which of the drinks was their favorite. In one Pepsi television commercial, an anouncer states that "in recent blind taste tests, more than one half of the surveyed preferred Diet Pepsi over Diet Coke." Suppose that out of those 120120, 6969 preferred Diet Pepsi. Test the hypothesis, using ?=0.01?=0.01 that more than half of all participants will select Diet Pepsi in a blind taste test by giving the following:
(a)    the test statistic     
(b)    the critical zz score    

The final conclustion is

A. We can reject the null hypothesis that p=0.5p=0.5 and accept that p>0.5p>0.5.
B. There is not sufficient evidence to reject the null hypothesis that p=0.5p=0.5.

Explanation / Answer

H0: P = 0.5

H1: P > 0.5

p = 69/120 = 0.575

a) The test statistic z = (p - P)/sqrt(P * (1 - P)/n)

                             = (0.575 - 0.5)/sqrt(0.5 * 0.5/120)

                            = 1.64

b) At alpha = 0.01, the critical value is z0.99 = 2.33

As the test statistic value is not greater than the critical value (1.64 < 2.33), so the null hypothesis is not rejected.

Option - B is the correct conclusion.

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