Question

1)

A report says that 82% of British Columbians over the age of 25 are high school graduates. A survey of randomly selected British Columbians included 1290 who were over the age of 25, and 1135 of them were high school graduates. Does the city’s survey result provide sufficient evidence to contradict the reported value, 82%?

Part i) What is the parameter of interest?

A. The proportion of all British Columbians (aged above 25) who are high school graduates.
B. Whether a British Columbian is a high school graduate.
C. All British Columbians aged above 25.
D. The proportion of 1290 British Columbians (aged above 25) who are high school graduates.

Part ii) Let pp be the population proportion of British Columbians aged above 25 who are high school graduates. What are the null and alternative hypotheses?

A. Null: p=0.88p=0.88. Alternative: p≠0.88p≠0.88.
B. Null: p=0.82p=0.82. Alternative: p=0.88p=0.88.
C. Null: p=0.82p=0.82. Alternative: p>0.82p>0.82.
D. Null: p=0.88p=0.88. Alternative: p>0.88p>0.88.
E. Null: p=0.82p=0.82. Alternative: p≠0.82p≠0.82 .
F. Null: p=0.88p=0.88. Alternative: p≠0.82p≠0.82.

Part iii) The PP-value is less than 0.0001. Using all the information available to you, which of the following is/are correct? (check all that apply)

A. The reported value 82% must be false.
B. Assuming the reported value 82% is correct, it is nearly impossible that in a random sample of 1290 British Columbians aged above 25, 1135 or more are high school graduates.
C. The observed proportion of British Columbians who are high school graduates is unusually high if the reported value 82% is correct.
D. The observed proportion of British Columbians who are high school graduates is unusually low if the reported value 82% is correct.
E. The observed proportion of British Columbians who are high school graduates is unusually high if the reported value 82% is incorrect.
F. The observed proportion of British Columbians who are high school graduates is unusually low if the reported value 82% is incorrect.
G. Assuming the reported value 82% is incorrect, it is nearly impossible that in a random sample of 1290 British Columbians aged above 25, 1135 or more are high school graduates.

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

A. There is sufficient evidence to contradict the reported value 82%.
B. There is insufficient evidence to contradict the reported value 82%.
C. There is a 5% probability that the reported value 82% is true.
D. Both A. and C.
E. Both B. and C.

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

A. The data suggest that reported value is correct when in fact the value is incorrect.
B. The data suggest that reported value is correct when in fact the value is correct.
C. The data suggest that reported value is incorrect when in fact the value is correct.
D. The data suggest that reported value is incorrect when in fact the value is incorrect.

Part vi) 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. Type II error only.
C. Both Type I and Type II errors.
D. Neither Type I nor Type II errors.

2)

(1 point) 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. Whether a person at UBC drinks coffee regularly.
B. The proportion of all people at UBC that drink 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=0.84p=0.84. Alternative: p≠0.84p≠0.84.
B. Null: p=0.84p=0.84. Alternative: p>0.80p>0.80.
C. Null: p=0.80p=0.80. Alternative: p>0.80p>0.80 .
D. Null: p=0.84p=0.84. Alternative: p>0.84p>0.84.
E. Null: p=0.80p=0.80. Alternative: p=0.84p=0.84.
F. Null: p=0.80p=0.80. Alternative: p≠0.80p≠0.80.

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 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. 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.
D. The observed proportion of people at UBC that drink coffee regularly is unusually low if the reported value 80% is incorrect.
E. The observed proportion of people at UBC that drink coffee regularly is unusually high if the reported value 80% is correct.
F. The observed proportion of people at UBC that drink coffee regularly is unusually high if the reported value 80% is incorrect.
G. The reported value 80% must be false.

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

A. 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%.
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 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 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%.

Part vi) 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. Both Type I and Type II errors.
C. Type I error only.
D. Neither Type I nor Type II errors.

3)Suppose some researchers wanted to test the hypothesis that living in the country is better for your lungs than living in a city. To eliminate the possible variation due to genetic differences, suppose they located five pairs of identical twins with one member of each twin living in the country, the other in a city. For each person, suppose they measured the percentage of inhaled tracer particles remaining in the lungs after one hour: the higher the percentage, the less healthy the lungs. Suppose they found that for four of the five twin pairs the one living in the country had healthier lungs.Is the alternative hypothesis one-sided or two-sided?one-sided
one-sided or two-sided
two-sided
none of these answersHere are the probabilities for the number of heads in five tosses of a fair coin:

# Heads	0	1	2	3	4	5
Probability	0.03125	0.15625	0.3125	0.3125	0.15625	0.03125

Compute the p-value and state your conclusion.p-value = 0.15625 + 0.03125 = 0.1875 and we have little evidence that individuals living in the country have healthier lungs than those individuals living in cities.
p-value = 0.03125 and we have little evidence that individuals living in the country have healthier lungs than those individuals living in cities.
p-value = 0.15625 and we have little evidence that individuals living in the country have healthier lungs than those individuals living in cities.
p-value = 0.15625 - 0.03125 = 0.125 and we have little evidence that individuals living in the country have healthier lungs than those individuals living in cities.

Answer 1