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, 59 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

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p > 0.5

n = 110

x = 59

= x / n = 59 / 110 = 0.5364

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

(a)

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.5364 - 0.5/ [(0.5 * 0.5) / 110]

= 0.763

Test statistic = 0.763

= 0.05

Z_0.05 = 1.645

Critical z score = 1.645