The 49 students in a class made blinded evaluations on pairs of cola drinks. For the 49 comparisons of Coke and Pepsi, Coke was preferred 29 times. Researchers want to know : in the populations that this sample represents, is there strong evidence that a majority prefers one of the two drinks?
a) Define the parameter of interest, state the null and alternative hypotheses corresponding to the researchers' questions.
b) Compute the test statistics corresponding to the hypothesis
c) Compute the p-value and interpret in terms of the researchers' questions.
d) compute the 99% confidence interval for the true value of p, the proportion of students who prefer Coke. Interpret the interval in context of the problem.
e) What information does the confidence interval give you that the hypothesis test does not?