Question

A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 80 subjects who participate in the study, 28 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)

a) Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the large-sample z statistic. (Round your answer to two decimal places.)

b) Report its P-value. (Round your answer to four decimal places.)

Answer 1

Test the claim that a majority of people prefer the taste of fresh-brewed coffee , We have to test

is the true proportion of the people who uses fresh-brewed coffee.

a) The estimated proportion of the population who prefer fresh-brewed coffee is

The large-sample z statistic is

At level, the critical value is . Since the statistic is greater than the critical value, we reject the null hypothesis at 95% confidence. Majority of people prefer (p >0.5) fresh-brewed coffee.(Right tailed Z-test).

b) The P-value is found using the test statistics.