According to a recent marketing campaign, drinkers of either Diet Coke or Diet Pepsi participated in blind taste tests to see which of the drinks was their favorite. In one Pepsi television commercial, an anouncer states that "in recent blind taste tests, at least one half of the surveyed preferred Diet Pepsi over Diet Coke." Suppose that in one of those taste tests, 5050 out of the 120120 participating preferred Diet Pepsi. Test the hypothesis, using α=0.05α=0.05 that at least half of all participants will select Diet Pepsi in a blind taste (hint: take HaHa to be that fewer than half prefer Diet Pepsi) test by giving the following: (a) the test statistic Recall the zz value that marks the start of the rejection region is the critical zz score; if you're lower tailed, it's the zz value that has left area of αα; if you're right tailed, it's the zz value whose area to the right is αα; if you're two-tailed, they're the values of the ±z±z value that −z−z has left area of α2α2 and zz has a right are of α2α2 ... note the divided by 2 part!! (b) the critical zz score The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that p=0.5p=0.5. B. We can reject the null hypothesis that p=0.5p=0.5 and accept that p<0.5p<0.5
According to a recent marketing campaign, drinkers of either Diet Coke or Diet Pepsi participated in blind taste tests to see which of the drinks was their favorite. In one Pepsi television commercial, an anouncer states that "in recent blind taste tests, at least one half of the surveyed preferred Diet Pepsi over Diet Coke." Suppose that in one of those taste tests, 5050 out of the 120120 participating preferred Diet Pepsi. Test the hypothesis, using α=0.05α=0.05 that at least half of all participants will select Diet Pepsi in a blind taste (hint: take HaHa to be that fewer than half prefer Diet Pepsi) test by giving the following:
(a) the test statistic
Recall the zz value that marks the start of the rejection region is the critical zz score; if you're lower tailed, it's the zz value that has left area of αα; if you're right tailed, it's the zz value whose area to the right is αα; if you're two-tailed, they're the values of the ±z±z value that −z−z has left area of α2α2 and zz has a right are of α2α2 ... note the divided by 2 part!!
(b) the critical zz score
The final conclusion is
A. There is not sufficient evidence to reject the null hypothesis that p=0.5p=0.5.
B. We can reject the null hypothesis that p=0.5p=0.5 and accept that p<0.5p<0.5.
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