Marty's Burger Barn provides a "Be A Glutton" option for all of their combo meals. This option is offered to all customers purchasing a combo meal for an additional charge of $0.35. Marty has determined that if a store is marketing the option properly, at least 70% of eligible customers will choose to "Be A Glutton".

Marty has asked for your help in evaluating the "Be A Glutton" performance at one of his locations. You have informed Marty that you intend to use a level of significance of 0.05 and that the appropriate confidence interval on p is guaranteed to have an error of 0.02 or less.

(a) What sample size will you use? You may assume that this sample size is used for the remainder of the problem.

(b) What is the probability of a Type II error when p = 0.65?

(c) Explain your answer to part (b) to Marty. Remember that he has no training in probability and statistics.

(d) After collecting appropriate data, you find that 1148 customers chose to "Be A Glutton". Compute P-value and determine the conclusion of the test.

(e) Build the 99% confidence interval that is appropriate for this test.