Question 1

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

Accepted Answer

A)  0.37 to 0.43 
B)  0.31 to 0.39 
C)  0.34 to 0.46 
D)  0.03 plus or minus 0.8 
E)  99% accurate 
A)  0.37 to 0.43 
B)  0.31 to 0.39 
C)  0.34 to 0.46 
D)  0.03 plus or minus 0.8 
E)  99% accurate C

Question 2

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.

Accepted Answer

A)  bias 
B)  confidence level 
C)  mean 
D)  parameter 
E)  statistic 
A)  bias 
B)  confidence level 
C)  mean 
D)  parameter 
E)  statistic D

Question 3

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)

Accepted Answer

A)  0.57 ± 0.00016. 
B)  0.57 ± 0.00032. 
C)  0.57 ± 0.013. 
D)  0.57 ± 0.025. 
E)  0.57 ± 0.03. 
A)  0.57 ± 0.00016. 
B)  0.57 ± 0.00032. 
C)  0.57 ± 0.013. 
D)  0.57 ± 0.025. 
E)  0.57 ± 0.03. D

Question 4

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?

Accepted Answer

A)  11.75 and 12.25 
B)  11.5 and 12.5 
C)  2.5 and 12 
D)  7 and 17 
E)  9.5 and 14.5 
A)  11.75 and 12.25 
B)  11.5 and 12.5 
C)  2.5 and 12 
D)  7 and 17 
E)  9.5 and 14.5

Question 5

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?

Accepted Answer

A)  Not at all, because the width of the confidence interval depends only on the sample size, and not on the population size. 
B)  Not at all, because the width of the confidence interval depends only on the sample size, and not on how the sample was obtained. 
C)  It would be wider because voluntary response polls have a bigger margin of error than simple random samples. 
D)  It would be narrower because voluntary response polls are less variable than simple random samples. 
E)  A confidence interval makes no sense for a voluntary response sample. 
A)  Not at all, because the width of the confidence interval depends only on the sample size, and not on the population size. 
B)  Not at all, because the width of the confidence interval depends only on the sample size, and not on how the sample was obtained. 
C)  It would be wider because voluntary response polls have a bigger margin of error than simple random samples. 
D)  It would be narrower because voluntary response polls are less variable than simple random samples. 
E)  A confidence interval makes no sense for a voluntary response sample.

Question 6

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?

Accepted Answer

A)  11.75 and 12.25 
B)  11.5 and 12.5 
C)  2.5 and 12 
D)  7 and 17 
E)  9.5 and 14.5 
A)  11.75 and 12.25 
B)  11.5 and 12.5 
C)  2.5 and 12 
D)  7 and 17 
E)  9.5 and 14.5

Question 7

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

Accepted Answer

A)  biased. 
B)  99%. 
C)  2.8. 
D)  smaller than 2.8. 
E)  larger than 2.8. 
A)  biased. 
B)  99%. 
C)  2.8. 
D)  smaller than 2.8. 
E)  larger than 2.8.

Question 8

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?

Accepted Answer

A)  ARCO graphite beats 95% of conventional motor oils. 
B)  The interval from 1% to 8.7% covers 95% of the mileage improvements observed in the tests. 
C)  The tests included 95% of all oil brands on the market. 
D)  The estimate that mileage improves somewhere between 1% and 8.7% came from a method that would catch the true improvement in 95% of all similar tests. 
E)  A mistake has been made, because 95% + 8.7% is more than 100%. 
A)  ARCO graphite beats 95% of conventional motor oils. 
B)  The interval from 1% to 8.7% covers 95% of the mileage improvements observed in the tests. 
C)  The tests included 95% of all oil brands on the market. 
D)  The estimate that mileage improves somewhere between 1% and 8.7% came from a method that would catch the true improvement in 95% of all similar tests. 
E)  A mistake has been made, because 95% + 8.7% is more than 100%.

Question 9

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)

Accepted Answer

A)  0.3115 ± 0.017. 
B)  0.623 ± 0.017. 
C)  0.3115 ± 0.0207. 
D)  0.623 ± 0.0207. 
E)  0.3115 ± 0.0267. 
A)  0.3115 ± 0.017. 
B)  0.623 ± 0.017. 
C)  0.3115 ± 0.0207. 
D)  0.623 ± 0.0207. 
E)  0.3115 ± 0.0267.

Question 10

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

Accepted Answer

A)  standard deviation. 
B)  margin of error. 
C)  confidence level. 
D)  sampling distribution. 
A)  standard deviation. 
B)  margin of error. 
C)  confidence level. 
D)  sampling distribution.

Question 11

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:

Accepted Answer

A)  0.16 to 0.20. 
B)  0.15 to 0.21. 
C)  0.14 to 0.22. 
D)  0.13 to 0.23. 
A)  0.16 to 0.20. 
B)  0.15 to 0.21. 
C)  0.14 to 0.22. 
D)  0.13 to 0.23.

Question 12

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

Accepted Answer

A)  the bias of the statistic. 
B)  the sampling distribution of the statistic. 
C)  the scale of measurement of the statistic. 
D)  the variability of the statistic. 
E)  the sampling error. 
A)  the bias of the statistic. 
B)  the sampling distribution of the statistic. 
C)  the scale of measurement of the statistic. 
D)  the variability of the statistic. 
E)  the sampling error.

Question 13

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:

Accepted Answer

A)  use a simple random sample of size less than 1,000. 
B)  use a simple random sample of size greater than 1,000. 
C)  use a confidence level less than 95 percent. 
D)  use a confidence level greater than 95 percent. 
E)  use a simple random sample of size greater than 1,000, and use a confidence level less than 95 percent. 
A)  use a simple random sample of size less than 1,000. 
B)  use a simple random sample of size greater than 1,000. 
C)  use a confidence level less than 95 percent. 
D)  use a confidence level greater than 95 percent. 
E)  use a simple random sample of size greater than 1,000, and use a confidence level less than 95 percent.

Question 14

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:

Accepted Answer

A)  0.86 ± 0.000231. 
B)  0.86 ± 0.0105. 
C)  0.86 ± 0.021. 
D)  0.86 ± 0.03. 
A)  0.86 ± 0.000231. 
B)  0.86 ± 0.0105. 
C)  0.86 ± 0.021. 
D)  0.86 ± 0.03.

Question 15

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?

Accepted Answer

A)  56 to 100 percent 
B)  54.4 to 57.6 percent 
C)  52.8 to 59.2 percent 
D)  51.2 to 60.8 percent 
A)  56 to 100 percent 
B)  54.4 to 57.6 percent 
C)  52.8 to 59.2 percent 
D)  51.2 to 60.8 percent

Question 16

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.

Accepted Answer

A)  Statistical inference 
B)  Normal mean theorem 
C)  Law of large numbers 
D)  Central limit theorem 
A)  Statistical inference 
B)  Normal mean theorem 
C)  Law of large numbers 
D)  Central limit theorem

Question 17

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?

Accepted Answer

A)  It would be smaller because it omits only 1 percent of the possible samples instead of 10 percent. 
B)  It would be the same because the sample is the same. 
C)  It would be larger because higher confidence requires a larger margin of error. 
D)  It is impossible to tell because the margin of error is random. 
E)  It is impossible to tell unless a census is taken. 
A)  It would be smaller because it omits only 1 percent of the possible samples instead of 10 percent. 
B)  It would be the same because the sample is the same. 
C)  It would be larger because higher confidence requires a larger margin of error. 
D)  It is impossible to tell because the margin of error is random. 
E)  It is impossible to tell unless a census is taken.

Question 18

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?

Accepted Answer

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. 
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.

Question 19

The confidence level is

Accepted Answer

A)  another name for the margin of error. 
B)  the probability that the actual parameter value is in your computed interval. 
C)  a probability that says how often in many samples the method would produce an interval that contains the actual parameter value. 
D)  the standard deviation of the sampling distribution. 
A)  another name for the margin of error. 
B)  the probability that the actual parameter value is in your computed interval. 
C)  a probability that says how often in many samples the method would produce an interval that contains the actual parameter value. 
D)  the standard deviation of the sampling distribution.

Question 20

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

Accepted Answer

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. 
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.

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

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)

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?

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?

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?

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

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?

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

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 _______________ 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.

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 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?

The confidence level is

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

Where Do Data Come From

Samples, Good and Bad

What Do Samples Tell Us

Sample Surveys in the Real World

Experiments, Good and Bad

Experiments in the Real World

Data Ethics

Measuring

Do the Numbers Make Sense

Graphs, Good and Bad

Displaying Distributions With Graphs

Normal Distributions

Describing Relationships: Scatterplots and Correlation

Describing Relationships: Regression, Prediction, and Causation

The Consumer Price Index and Government Statistics

Thinking About Chance

Probability Models

Simulation

The House Edge: Expected Values

What Is a Test of Significance

Use and Abuse of Statistical Inference

Two-Way Tables and the Chi-Square Test

Filters

Exam 21: What Is a Confidence Interval

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

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)

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?

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?

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?

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

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?

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

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 _______________ 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.

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 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?

The confidence level is

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

Where Do Data Come From

Samples, Good and Bad

What Do Samples Tell Us

Sample Surveys in the Real World

Experiments, Good and Bad

Experiments in the Real World

Data Ethics

Measuring

Do the Numbers Make Sense

Graphs, Good and Bad

Displaying Distributions With Graphs

Normal Distributions

Describing Relationships: Scatterplots and Correlation

Describing Relationships: Regression, Prediction, and Causation

The Consumer Price Index and Government Statistics

Thinking About Chance

Probability Models

Simulation

The House Edge: Expected Values

What Is a Test of Significance

Use and Abuse of Statistical Inference

Two-Way Tables and the Chi-Square Test

Filters