Question 1: A study was conducted to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours.
A similar study conducted a year earlier estimated that μ, the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year.
Using a 95% confidence interval of (7.7, 9.3), which of the following is an appropriate conclusion?
A. The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
B. The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.
C. The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
D. The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.
E. None of the above. You cannot draw a conclusion because the only way to reach a conclusion is to find the p-value of the test.
Question 2
Which of the following facts about the p-value of a test is correct? Check all that apply.
A. The p-value is calculated under the assumption that the null hypothesis is true.
B. The smaller the p-value, the more evidence the data provide against H0.
C. The p-value can have values between -1 and 1.
Question 3
In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is the most important problem facing this country today?" Roughly 19% of those sampled answered "the war in Iraq" (while the rest answered economy/jobs, terrorism, healthcare, etc.). Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country.
We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.
Which of the following are the appropriate hypotheses in this case?
A. H0: p = 0.19 vs. Ha: p < 0.19
B. H0: p = 0.19 vs. Ha: p > 0.19
C. H0: p < 0.25 vs. Ha: p = 0.25
D. H0: p = 0.25 vs. Ha: p < 0.25
E. H0: p = 0.25 vs. Ha: p ≠ 0.25
Question 4
In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is the most important problem facing this country today?" Roughly 19% of those sampled answered "the war in Iraq" (while the rest answered economy/jobs, terrorism, healthcare, etc.). Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country.
We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.
The following output is available for this test:
Which of the following is the best conclusion based on the output?
A. We have extremely strong evidence to reject H0.
B. We have extremely strong evidence to reject Ha.
C. We have moderately strong evidence to reject H0.
D. There is a probability of 0 that H0 is correct.
E. There is a probability of 0 that Ha is correct.
Question 5
An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally with the mean μ = 10 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.
We want to determine if these data provide enough evidence to conclude that the mean volume per cup is below the target level.
Which one of the two outputs represents the correct way to conduct this test?
A
B
Question 6
An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally with the mean μ = 10 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.
Below is the output:
Which of the following represents the correct conclusion we can make based on the output (and at the usual significance level of .05)?
A. The data provide enough evidence to reject H0 and to conclude that the mean volume per cup is lower than the target level of 10 oz.
B. The data provide enough evidence to accept H0 and to conclude that the mean volume per cup is at the target level of 10 oz.
C. The data do not provide enough evidence to reject H0, so we accept it, and conclude that the mean volume per cup is at the target level of 10 oz.
D. The data do not provide enough evidence to reject H0, nor to conclude that the mean volume per cup is lower than the target level of 10 oz.
Question 7
An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally with the mean μ = 10 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.
In this problem, we have made slight changes to the "coffee machine" story above. In which of the options below is the change such that it would be inappropriate to conduct a hypothesis test for: H0: μ = 10 vs. Ha: μ < 10. Check all that apply.
A. An automatic coffee machine dispenses cups of coffee whose volume per cup varies according to a distribution with mean μ = 10 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.
B. An automatic coffee machine dispenses cups of coffee whose volume per cup varies according to a distribution with mean μ = 10 oz. A quality-control researcher randomly selects 40 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.
C. An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally with mean μ = 10 oz. and standard deviation σ = 0.23 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz.
D. An automatic coffee machine dispenses cups of coffee whose volume per cup varies according to a distribution with mean μ = 10 oz. and standard deviation σ = 0.23 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz.