Question

Coca-Cola drinkers participated in a blind taste test where they were asked to taste unmarked cups of Pepsi and Coke and were asked to select their favorite. In one Pepsi television commercial, an announcer states that "in recent blind taste tests, more than half the Diet Coke drinkers surveyed said they preferred the taste of Diet Pepsi". Suppose 100 Diet Coke drinkers took the Pepsi Challenge and 56 preferred the taste of Diet Pepsi. Test the hypothesis that more than half of all Diet Coke drinkers will select Diet Pepsi in the blind taste test. Use α = .05.

Answer 1

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

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.56 - 0.5)/sqrt(0.5*(1-0.5)/100)
z = 1.2

P-value Approach
P-value = 0.1151
As P-value >= 0.05, fail to reject null hypothesis.