Coke/Pepsi Taste Test
Suppose 500 people participate in a blind Coke/Pepsi taste test, and 285 of them prefer Coke while the other 215 of them prefer Pepsi.
(a) If we conduct inference (creating a confidence interval or conducting a hypothesis test) using this data, should we use the formulas for a single proportion or a difference in proportions?
(b) If we want to test whether the preferences are equally split between Coke and Pepsi, what is the null hypothesis?
(c) In terms of the outcome of the test, does it matter whether we define p to be the proportion of people who prefer Coke or the proportion of people who prefer Pepsi?