Question

According to a recent marketing campaign, 100 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 100 , 59 preferred Diet Pepsi. Test the hypothesis, using α=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 P -value

The final conclustion is

A. We can reject the null hypothesis that p=0.5 p=0.5 and accept that p>0.5.

B. There is not sufficient evidence to reject the null hypothesis that p=0.5.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.5
Alternative Hypothesis, Ha: p > 0.5

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.59 - 0.5)/sqrt(0.5*(1-0.5)/100)
z = 1.8

P-value Approach
P-value = 0.0359

As P-value >= 0.01, fail to reject null hypothesis.
B. There is not sufficient evidence to reject the null hypothesis that p=0.5.