According to a recent marketing campaign, 110 drinkers of either Diet Coke or Di

Question

According to a recent marketing campaign, 110 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 110, 40 preferred Diet Pepsi. Test the hypothesis, using alpha = 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 z score The final conclusion is A. We can reject the null hypothesis that p 0.5 and accept that p 0.5. B. There is not sufficient evidence to reject the null hypothesis that p 0.5.

Explanation / Answer

1.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.5
Ha:   p   <   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.363636364      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.047673129      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.860387768   [ANSWER, TEST STATISTIC]  
          
***********************************  
          
As this is a    1   tailed test, then, getting the critical value using table/technology, at 0.01 level,

zcrit = -2.326 [ANSWER]

************************************

As |z| = 2.86 > 2.326, we reject Ho.

Then, the final conclusion is OPTION A. [ANSWER, A]

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