Statistics students were conducting a test to see if people could taste the difference between Coke and Pepsi. They fill two cups with Coke and a third with Pepsi. They then asked their subjects which cola tasted different than the other two. Of the 64 people they tested, 22 were able to correctly identify which of the three cups of colas tasted different (i.e., which of the three cups was the Pepsi).
a. Conduct a simulation-based test of significance to determine if the proportion of people that correctly identify the different cola is greater than what would occur by just randomly guessing. Give the hypotheses, the p-value, and a conclusion.
b. Using the standard deviation from your null distribution in part (a), determine a 2SD confidence interval for the population proportion that can correctly identify the cola that is different?
c. Is the proportion under your null hypothesis from part (a) contained in your confidence interval from part (b)? Explain how this relates to the size of your p-value from part (a).