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.** Whether a person at UBC drinks coffee
regularly.

**C.** The proportion of people at UBC that drink
coffee regularly out of the 810 surveyed.

**D.** All people at UBC that drinks coffee
regularly.

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

**A.** Null: p=0.80p=0.80. Alternative:
p=0.84p=0.84.

**B.** Null: p=0.80p=0.80. Alternative:
p≠0.80p≠0.80.

**C.** Null: p=0.84p=0.84. Alternative:
p>0.80p>0.80.

**D.** Null: p=0.80p=0.80. Alternative:
p>0.80p>0.80 .

**E.** Null: p=0.84p=0.84. Alternative:
p≠0.84p≠0.84.

**F.** Null: p=0.84p=0.84. Alternative:
p>0.84p>0.84.

**Part iii)** The PP-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 high if the reported value 80%
is incorrect.

**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 correct.

**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 low if the reported value 80%
is correct.

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

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

**B.** we should 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 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%.

**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 exceeds the reported value
80%.

**D.** 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%.

**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 II error only.

**B.** Type I error only.

**C.** Neither Type I nor Type II errors.

**D.** Both Type I and Type II errors.

Answer #1

i)**A.** The proportion of all people at UBC that
drink coffee regularly.

ii) **D.** Null: p=0.80. Alternative: p>0.80

iii)**D.** The observed proportion of people at UBC
that drink coffee regularly is unusually high if the reported value
80% is correct.

**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.

iv)

**B.** we should reject the null hypothesis.

v)

**A.** There is sufficient evidence to support
opening a store at UBC.

vi)

**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 exceeds the reported value
80%.

vii)

**B.** Type I error only.

2)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...

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