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Exam 21: What Is a Confidence Interval

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Question 1

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If we take a simple random sample of size n = 500 from a population of size 500,000, the variability of our estimate will be

A) less than the bias.
B) approximately the same as the variability for a sample of size n = 500 from a population of size 50,000,000.
C) plus or minus 0.1%.
D) much greater than the variability for a sample of size n = 500 from a population of size 50,000,000.
E) much less than the variability for a sample of size n = 500 from a population of size 50,000,000.

F) A) and B)
G) B) and D)

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Question 2

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A poll of 1,006 American adults found that 30 percent believe the government should do "a great deal" about global warming. Taking the poll's sample to be a simple random sample of all American adults, which of these is a correct 95 percent confidence statement?

A) With 95 percent confidence (but not certainty) , the percent of the sample who believe the government should do "a great deal" about global warming is between 28.6 and 31.4 percent.
B) With 95 percent confidence (but not certainty) , the percent of the sample who believe the government should do "a great deal" about global warming is between 27.2 and 32.8 percent.
C) With 95 percent confidence, the percent of all American adults who believe the government should do "a great deal" about global warming is between 28.6 and 31.4 percent.
D) With 95 percent confidence, the percent of all American adults who believe the government should do "a great deal" about global warming is between 27.2 and 32.8 percent.

E) C) and D)
F) All of the above

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Question 3

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The weights for a population of North American raccoons have a bell-shaped frequency curve with a mean of about 12 pounds and a standard deviation of about 2.5 pounds. About 95% of the mean weights from samples of size 100 raccoons from this population fall between what two values?

You choose a simple random sample of 2000 women over 18 years of age from the New York City metropolitan area; 623 of them are single. A 90% confidence interval for the proportion of all adult women in the New York area who are single is (approximately)

The name for the pattern of values that a statistic takes when we sample repeatedly from the same population is

The _______________ says that, as we take more and more observations at random from any population, the distribution of the mean of these observations eventually gets close to a Normal distribution.

The confidence level is

A surprising fact: only 56% of all teens use a password on their mobile device. If a poll chooses a simple random sample of 1000 teens and asks if they use a password on their mobile device, the percent who say "Yes" will vary if the sample is repeated. In fact, the percent "Yes" in many samples will follow a normal distribution with mean 56% and standard deviation 1.6%. Which of these ranges of outcomes contains 95 percent of all the results of a large number of polls of 1,000 teens?

A surprising fact: only 56% of all teens use a password on their mobile device. If a poll chooses a simple random sample of 1000 teens and asks if they use a password on their mobile device, the percent who say "Yes" will vary if the sample is repeated. In fact, the percent "Yes" in many samples will follow a normal distribution with mean 56% and standard deviation 1.6%. The variation from sample to sample, when the poll is repeated, is described by the standard deviation (1.6 percent) . We would like this variation to be small so that repeated polls give almost the same result. To reduce the standard deviation, we could:

A recent Gallup Poll interviewed a random sample of 1523 adults. Of these, 868 bought a lottery ticket in the past year. A 95% confidence interval for the proportion of all adults who bought a lottery ticket in the past year is (assume Gallup used a simple random sample)

A November 2015 poll of size n = 1021 had a sample proportion = 0.86 disapproving of Congress. If this is regarded as a simple random sample, then a 95 percent confidence interval for the proportion p of all adults who disapprove of Congress is closest to:

The formula for a 95% confidence interval for a population proportion is given by ) The entire "plus or minus part" of this confidence interval is also called the

The student newspaper at a college asks a simple random sample of 250 undergraduates, "Do you favor eliminating supplemental fees for lab courses?" In all, 150 of the 250 are in favor of eliminating such fees. The ___________ you want to estimate is the proportion p of all undergraduates who favor eliminating the supplemental fees for lab courses.

If the 1,017 people in the previous question had called a 900 number to give their opinions, how would this have affected the response?

An ad for ARCO graphite motor oil says (really) : "Based on a 95% confidence level, our tests achieved between 1% and 8.7% mileage improvement" as compared with a conventional motor oil. What does the phrase "95% confidence level" mean here?

The margin of error for a 95% confidence interval is 2.8. If we decrease the confidence level to 90%, the margin of error will be

A member of the city government thinks that 90 percent confidence isn't enough. He wants to be 99 percent confident. How would the margin of error of a 99 percent confidence interval compare with the 90 percent interval found for the same sample?

A recent survey of 54,000 randomly selected U.S. adults studied the religious affiliation of Americans. The survey interviewed 645 people in Oregon. Suppose that this is a simple random sample of adult residents of Oregon. Of these 645 people, 116 said they claimed no religious identity. A 95 percent confidence interval for the proportion of all residents of Oregon who claim no religious identity is closest to:

The weights for a population of North American raccoons have a bell-shaped frequency curve with a mean of about 12 pounds and a standard deviation of about 2.5 pounds. About 95% of the weights for individual raccoons in this population fall between what two values?

We observe = 0.4. If the standard deviation of the sampling distribution of is 0.03, what is the 95% confidence interval for p?