(7 points) You run a coffee shop which is testing a new type of espresso maker. Your business dependson having repeat customers, so you give away...

7. (7 points) You run a coffee shop which is testing a new type of espresso maker. Your business dependson having repeat customers, so you give away samples of the espresso for free. You ask people whetheror not they would purchase the espresso again at the current price you are selling it for. You have 144customers come in the door and 48 of them state that they would purchase the espresso again. Youtried the espresso yourself and thought that 30% of people would buy the coffee again.

(a) You want to compare your sample to your original hypothesis. You are agnostic about the directionof the claim. What is the hypothesis that you want to test?

(b) Write down the test-statistic associated with this hypothesis.

(c) Test your hypothesis. What is your conclusion?(d) Would the results of your hypothesis test change if you had more people but the same proportionof successes? Briefly describe how the results would change.