Question

According to a recent marketing campaign, 120 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 120, 72 preferred Diet Pepsi. Test the hypothesis, using α=0.05 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

Answer 1

H0: p = 0.50

Ha: p > 0.50

a)

Sample proportion $\hat{p}$ = 72 / 120 = 0.60

Test statistics

z = $\hat{p}$ - p / sqrt(p(1-p) / n)

= 0.60 - 0.50 / sqrt(0.5 * 0.5 / 120)

= 2.19

b)

At 0.05 level,

Critical value = 1.645