In a recent taste test, 1017 out of 1250 people could not tell the difference between a popular soda’s original flavor and the new calorie-free flavor. The company claims that more than 80%

Question

of the people cannot tell the difference. Find a test statistic for the proportion. I know the answer is z = 1.20, I'm just not sure how to get that answer. Could someone explain?

Answer 1

This seems to be a binomial distribution. There are only two possible outcomes: people can tell the difference; or people can’t tell the difference. The company claim that over 80% can’t tell the difference, so that’s 80% of 1250=1000. If we put p=0.80 then np is the mean=1000 and the variance is np(1-p)=1000(0.20)=200, the square root being the standard deviation=√200=14.14 approx. The Z score for 1017 is (1017-1000)/14.14=17/14.14=1.20.