McBeans magazine recently published a news article about caf

McBeans magazine recently published a news article about caffeine consumption in universities that claims that 80% of people at universities drink coffee regularly. Moonbucks, a popular coffee chain, is interested in opening a new store on NYU campus. After reading McBeans\' article, they will consider opening a store in NYU if more than 80% of the people in NYU drink coffee regularly. A random sample of people from NYU was taken, and it was found that 680 out of 810 survey participants considered themselves as regular coffee drinkers. Does Moonbucks\' survey result provide sufficient evidence to support opening a store at NYU?

Part i) What is the parameter of interest?

A. Whether a person at NYU drinks coffee regularly.
B. The proportion of all people at NYU that drink coffee regularly.
C. All people at NYU that drinks coffee regularly.
D. The proportion of people at NYU that drink coffee regularly out of the 810 surveyed.

Part ii) The P-value is found to be about 0.0025. Using all the information available to you, which of the following is/are correct? (check all that apply)

A. The observed proportion of people at NYU that drink coffee regularly is unusually high if the reported value 80% is incorrect.
B. The observed proportion of people at NYU that drink coffee regularly is unusually low if the reported value 80% is incorrect.
C. The observed proportion of people at NYU that drink coffee regularly is unusually low if the reported value 80% is correct.
D. Assuming the reported value 80% is correct, there is a 0.0025 probability that in a random sample of 810, at least 680 of the people at NYU regularly drink coffee.
E. Assuming the reported value 80% is incorrect, there is a 0.0025 probability that in a random sample of 810, at least 680 of the people at NYU regularly drink coffee
F. The observed proportion of people at NYU that drink coffee regularly is unusually high if the reported value 80% is correct.
G. The reported value 80% must be false.

Part iii) Which of the following scenarios describe the Type II error of the test?

A. The data provide sufficient evidence to support opening a store at NYU when in fact the true proportion of NYU people who drink coffee regularly exceeds the reported value 80%.
B. The data provide sufficient evidence to support opening a store at NYU when in fact the true proportion of NYU people who drink coffee regularly is equal to the reported value 80%.
C. The data do not provide sufficient evidence to support opening a store at NYU when in fact the true proportion of NYU people who drink coffee regularly is equal to the reported value 80%.
D. The data do not provide sufficient evidence to support opening a store at NYU when in fact the true proportion of NYU people who drink coffee regularly exceeds the reported value 80%.

Solution

Since the P-value is 0.0025 which is very small, So for a confidence level of 0.05 the claim is rejected

So A is correct

Also by defnition of P-value D is also correct