Error probabilities and power

Asha owns a car wash and is trying to decide whether or not to purchase a vending machine so customers can buy coffee while they wait. She'll get the machine if she's convinced that more than

30 %

of her customers would buy coffee. She plans on taking a random sample of

n

customers and asking them whether or not they would buy coffee from the machine, and she'll then do a significance test using

α = 0.05

to see if the sample proportion who say "yes" is significantly greater than

30 %

Which situation below would result in the highest power for her test?

(Choice A)
She uses a sample size of $n = 100$ ‍, and $32 %$ ‍ of all customers would actually buy coffee.
(Choice B)
She uses a sample size of $n = 200$ ‍, and $32 %$ ‍ of all customers would actually buy coffee.
(Choice C)
She uses a sample size of $n = 50$ ‍, and $50 %$ ‍ of all customers would actually buy coffee.
(Choice D)
She uses a sample size of $n = 200$ ‍, and $50 %$ ‍ of all customers would actually buy coffee.

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 10

Problem