Researchers polled residents in Kent and Sussex counties and asked if they were in favor of increasing funding for the arts. In a random sample of 100 residents from Sussex County, 22% supported the increase and in a random sample of 100 residents from Kent County, 26% supported the increase. A 95% confidence interval for the difference (ps - pk) was calculated as -0.04 ± 0.12. Which of the following is the best interpretation of the interval? ± −0.04±0.12 a We are 95% confident that the difference in the sample proportions of voters in districts Sussex County and Kent County who favor an increase in state spending for the arts is between −0.16 and 0.08. b We are 95% confident that the difference in the proportions of all voters in Sussex County and Kent County who favor an increase in state spending for the arts is between −0.16 and 0.08. c We are 95% confident that the majority of all voters in the state favor an increase in state spending for the arts. d We are 95% confident that the proportion of all voters in the state who favor an increase in state spending for the arts is between −0.16 and 0.08. e We are 95% confident that less than half of all voters in the state favor an increase in state spending for the arts.
Researchers polled residents in Kent and Sussex counties and asked if they were in favor of increasing funding for the arts. In a random sample of 100 residents from Sussex County, 22% supported the increase and in a random sample of 100 residents from Kent County, 26% supported the increase. A 95% confidence interval for the difference (ps - pk) was calculated as -0.04 ± 0.12. Which of the following is the best interpretation of the interval?
±
−0.04±0.12
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a
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We are 95% confident that the difference in the sample proportions of voters in districts Sussex County and Kent County who favor an increase in state spending for the arts is between −0.16 and 0.08.
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b
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We are 95% confident that the difference in the proportions of all voters in Sussex County and Kent County who favor an increase in state spending for the arts is between −0.16 and 0.08.
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c
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We are 95% confident that the majority of all voters in the state favor an increase in state spending for the arts.
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d
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We are 95% confident that the proportion of all voters in the state who favor an increase in state spending for the arts is between −0.16 and 0.08.
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e
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We are 95% confident that less than half of all voters in the state favor an increase in state spending for the arts.
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In a lightbulb factory, an administrator selects a random sample of bulbs produced on assembly line A and a random sample of bulbs produced on assembly line B. The administrator calculates the proportion of malfunctioning bulbs produced by each assembly line and finds that the difference between them (A - B) is 0.008. A researcher conducted a hypothesis test with the following hypotheses:
H0: The proportion of malfunctioning bulbs from assembly line A is the sample as the proportion of malfunctioning bulbs from assembly line B.
HA: The proportion of malfunctioning bulbs from assembly line A is greater than the proportion of malfunctioning bulbs from assembly line B.
She found a P-value of 0.016. What is the best interpretation of this P-value?
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a
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If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at least 0.008 is 0.016.
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b
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If there is a difference of 0.016 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.008.
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c
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If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.008 is 0.016.
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d
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If there is a difference of 0.008 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.016.
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e
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If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at most 0.008 is 0.016.
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A police officer uses a breathalyzer to test the blood alcohol content of drivers suspected of a DUI. The driver will be arrested if the officer believes that the driver is drunk, according to the results of the breathalyzer. The hypotheses can be stated as follows:
H0 : The driver is not drunk.
Ha : The driver is drunk.
Which of the following best describes the power of the test?
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a
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The probability of arresting a driver who is drunk.
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b
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The probability of not arresting a driver who is not drunk.
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c
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The probability of not arresting a driver who is drunk.
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d
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The probability of arresting a driver who is not drunk.
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e
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The probability that the breathalyzer is working correctly.
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A one-sided hypothesis test is to be performed with a significance level of 0.05. Suppose that the null hypothesis is false. If a significance level of 0.01 were to be used instead of a significance level of 0.05, which of the following would be true?
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a
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Neither the probability of a Type II error nor the power of the test would change.
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b
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The probability of a Type II error would decrease and the power of the test would increase.
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c
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Both the probability of a Type II error and the power of the test would increase.
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d
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The probability of a Type II error would increase and the power of the test would decrease.
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e
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Both the probability of a Type II error and the power of the test would decrease.
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