A plan for an executive travelers’ club has been developed by an airline on the premise that 5⁢% of its current customers would qualify for membership. A random sample of 500 customers yielded 40 who...

A plan for an executive travelers’ club has been developed by an airline on the premise that 5⁢% of its current customers would qualify for membership. A random sample of 500 customers yielded 40 who would qualify.

a) Using this data, test at level .01 the null hypothesis that the company’s premise is correct against the alternative that it is not correct.

b) What is the probability that when the test of part (a) is used, the company’s premise will be judged correct when in fact 10⁢% of all current customers qualify?

c) What should the sample size be to ensure that Beta(0.1) = 0.01? Use alpha = 0.01.