Statistics students conducted 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 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.
a. Determine a 95% theory-based confidence interval for the population proportion that can correctly identify the cola that is different?
b. What is the margin of error from your interval from part (a)?