An 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 60 subject sample who participate in the study, 21 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed 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 and its P-value.
b. Draw a sketch of the standard Normal curve and mark the location of your z statistic. Shade the appropriate area that corresponds to the P-value.
c. Is your result significant at the 5% level? What is your practical conclusion?
I think that I'm supposed to use a plus-four confidence interval test here, but it says that the qualifications are a sample of larger than 10 and a confidence interval of more than 90%. Do you just automatically do these even if you don't have a given confidence interval? Do you assume it's more than 90%?