Customers who participate in a store's free loyalty card program save money on their purchases but allow the store to keep track of their shopping habits and potentially sell these data to third parties. A Pew Internet & American Life Project Survey (January 2016) revealed that half (225) of a random sample of 250 U.S. adults would agree to participate in a store loyalty card program, despite the potential for information sharing.
a. Estimate the true proportion of all U.S. adults who would agree to participate in a store loyalty card program, despite the potential for information sharing.
b. Form a 90% confidence interval around the estimate, part a.
c. Provide a practical interpretation of the confidence interval, part b. Your answer should begin with, "We are 90% confident . . ."
d. Explain the theoretical meaning of the phrase, "We are 90% confident."