Question

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 UBC campus. After reading McBeans' article, they will consider opening a store in UBC if more than 80% of the people in UBC drink coffee regularly. A random sample of people from UBC 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 UBC?

Part i) What is the parameter of interest?

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

Part ii) Let p$p$ be the population proportion of people at UBC that drink coffee regularly. What are the null and alternative hypotheses?

A. Null: p=0.80$p=0.80$. Alternative: p>0.80$p>0.80$ .
B. Null: p=0.84$p=0.84$. Alternative: p≠0.84$p\ne 0.84$.
C. Null: p=0.84$p=0.84$. Alternative: p>0.80$p>0.80$.
D. Null: p=0.80$p=0.80$. Alternative: p≠0.80$p\ne 0.80$.
E. Null: p=0.84$p=0.84$. Alternative: p>0.84$p>0.84$.
F. Null: p=0.80$p=0.80$. Alternative: p=0.84$p=0.84$.

Part iii) The P$P$-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 UBC that drink coffee regularly is unusually low if the reported value 80% is correct.
B. 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 UBC regularly drink coffee
C. The observed proportion of people at UBC that drink coffee regularly is unusually low if the reported value 80% is incorrect.
D. The observed proportion of people at UBC that drink coffee regularly is unusually high if the reported value 80% is incorrect.
E. 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 UBC regularly drink coffee.
F. The reported value 80% must be false.
G. The observed proportion of people at UBC that drink coffee regularly is unusually high if the reported value 80% is correct.

Part iv) Based on the P$P$-value (approximately 0.0025) obtained, at the 5% significance level, ...

A. we should reject the null hypothesis.
B. we should not reject the null hypothesis.

Part v) What is an appropriate conclusion for the hypothesis test at the 5% significance level?

A. There is sufficient evidence to support opening a store at UBC.
B. There is insufficient evidence to support opening a store at UBC.
C. There is a 5% probability that the reported value 80% is true.
D. Both A. and C.
E. Both B. and C.

Part vi) 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 UBC when in fact the true proportion of UBC people who drink coffee regularly exceeds the reported value 80%.
B. The data provide sufficient evidence to support opening a store at UBC when in fact the true proportion of UBC 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 UBC when in fact the true proportion of UBC 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 UBC when in fact the true proportion of UBC people who drink coffee regularly exceeds the reported value 80%.

Part vii) Based on the result of the hypothesis test, which of the following types of errors are we in a position of committing?

A. Type I error only.
B. Both Type I and Type II errors.
C. Type II error only.
D. Neither Type I nor Type II errors.