Deck 7: Survey Sampling and Inference

Question 1

Frances is interested in whether students at his college would like to see a portion of the campuspreserved as green space. Using student numbers, he randomly contacts 300 students and receivesa response from 75. Of those who responded, 64% favored the preservation of green space oncampus. This scenario is describing what type of sampling bias?

A) Survey bias
B) Nonresponse bias
C) Measurement bias
D) Voluntary response bias

Answer 1

Nonresponse bias

Question 2

A random sample of 830 adult television viewers showed that 52% planned to watch sportingevent X. The margin of error is 3 percentage points with a 95% confidence. Does the confidenceinterval support the claim that the majority of adult television viewers plan to watch sporting eventX? Why?

A)No; the confidence interval means that we are 95% confident that the population proportionof adult television viewers who plan to watch sporting event X is between 49% and 55%. Thetrue proportion could be less than 50%.
B)Yes; the confidence interval means that we are 95% confident that the population proportionof adult television viewers who plan to watch sporting event X is between 49% and 55%.Since the confidence interval is mostly above 50% it is likely that the true proportion is greaterthan 50%.
C)No; the confidence interval means that we are 95% confident that the population proportionof adult television viewers who plan to watch sporting event X is between 50.5% and 53.5%.The lower limit of the confidence interval is just too close to 50% to say for sure.
D)Yes; the confidence interval means that we are 95% confident that the population proportionof adult television viewers who plan to watch sporting event X is between 50.5% and 53.5%.
This is strong evidence that the true proportion is greater than 50%

Answer 2

No; the confidence interval means that we are 95% confident that the population proportionof adult television viewers who plan to watch sporting event X is between 49% and 55%. Thetrue proportion could be less than 50%.

Question 3

Use the following information to answer the question. A pollotarian is a person who eats poultry but no red meat. A
wedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is to
be held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population of
about 200,000.


-Suppose the wedding planner assumes that 5% of the guests will be pollotarian so she orders 15pollotarian meals. What is the approximate probability that more than 5% of the guests arepollotarian and therefore she willnot have enoughpollotarian meals? Round to the nearestthousandth.

A) 0.421
B) 0.079
C) 0.489
D) None of these

Answer 3

0.079

Question 4

Which of the following statements is not true about a sampling distribution?

A) It is the probability distribution of a statistic.
B) It gives characteristics of the estimator, such as bias and precision.
C) It is used for making inferences about a sample.
D) It gives probabilities for a statistic.

Question 5

The mean age of all the U. S. vice presidents when they took office would be a_{--------------------} .

A) Statistic
B) Sample
C) Population
D) Parameter

Question 6

Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence increases the margin of error will_{--------------------} and the confidence interval will_{--------------------}
Be . A larger sample size will improve the accuracy of the confidence interval,
Therefore margin of error will_{--------------------} and the confidence interval will be _{--------------------}

A) Decrease, narrower. Increase, wider.
B) Decrease, wider. Increase, narrower.
C) Increase, wider. Decrease, narrower.
D) Increase, narrower. Decrease, wider.

Question 7

Which of the following statements is true about the confidence interval for a population proportion?

A) The confidence interval for a proportion will always contain the true population proportion.
B) The confidence interval for a proportion does not need a specified confidence level.
C) It is equal to the sample proportion plus or minus a calculated amount called the margin of error.
D) It is equal to the population proportion plus or minus a calculated amount called the standard error.

Question 8

There are four colors in a bag containing 600 plastic chips. It is known that 34% of the chips areyellow. On average, how many chips from a random sample of 30 (with replacement) would beexpected to be yellow? Round to the nearest whole chip.

A) About 5
B) Not enough information to determine expected value.
C) About 10
D) About 16

Question 9

According to a snack cracker manufacturer, a batch of butter crackers has a defect rate of 6%.Suppose a quality inspector randomly inspects 400 crackers. Complete the following statement: The quality inspector should expect_{--------------------}defective crackers, give or take_{--------------------}crackers.

A) 45; 6
B) 48; 5
C) 25; 12
D) 24; 5

Question 10

Use the following information to answer the question. In a recent poll of 1100 randomly selected home delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once.

-Report the 95% confidence interval for the proportion of all home delivery truck drivers who haveencountered an aggressive dog on the job at least once. (Round final calculations to the nearesttenth of a percent)

A) (23.4%, 28.6%)
B) (20.7%, 31.3%)
C) (24.7 %, 27.3%)
D) None of these

Question 11

If it is being used to make inferences about a population, a good statistic (or estimator) should

A) Show correlation.
B) Be accurate and precise.
C) Always equal the population parameter.
D) None of these.

Question 12

Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence increases the margin of error will_{--------------------} and the confidence interval be_{--------------------} . A larger sample size will improve the accuracy of the confidence interval,
Therefore margin of error will _{--------------------}and the confidence interval will be_{--------------------}

A) Decrease, narrower. Increase, wider.
B) Increase, narrower. Decrease, wider.
C) Decrease, wider. Increase, narrower
D) Increase, wider. Decrease, narrower.

Question 13

The collection of the ages of all the U.S. first ladies when they married is a_{--------------------} .

A) Population
B) Statistic
C) Sample
D) Parameter

Question 14

Which of the following statements is true about the confidence interval for a population proportion?

A) The confidence interval for a proportion will always contain the true population proportion.
B) It is equal to the sample proportion plus or minus a calculated amount called the margin of error.
C) It is equal to the population proportion plus or minus a calculated amount called the standard error.
D) The confidence interval for a proportion does not need a specified confidence level.

Question 15

Suppose that the age of all the U.S. first ladies when they married was recorded. The mean age of U.S. first ladies when they married would be a_{--------------------} .

A) Sample
B) Population
C) Statistic
D) Parameter

Question 16

A polling agency wants to determine the size of a random sample needed to estimate theproportion of homeowners who have an electronic home security system. The estimate should havemargin of error no more than 4 percentage points at a 95% level of confidence. Choose the mostconservative answer that is closest to your calculated number, rounding to the nearest wholeperson.

A) They should poll at least 1100 people.
B) They should poll at least 600 people.
C) They should poll at least 1000 people.
D) They should poll at least 500 people.

Question 17

Use the following information to answer the question. A pollotarian is a person who eats poultry but no red meat. Awedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is tobe held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population ofabout 200,000.

-On average, what proportion of the guests would be expected to be pollotarian, give or take how many? Round to the nearest whole person.

A) 20 people, give or take 5 people
B) 15 people, give or take 4 people
C) 11 people, give or take 3 people
D) There is not enough information given to calculate expected value.

Question 18

Use the following information to answer the question. A pescatarian is a person who eats fish and seafood but no other
animal. An event planner does some research and finds that approximately 2.75% of the people in the area where a large
event is to be held are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the local
population of about 150,000.

-On average, what proportion of the guests would be expected to be pescatarian, give or take how many? Round to the nearest whole person.

A) There is not enough information given to calculate expected value.
B) 8 people, give or take 4 people
C) 7 people, give or take 3 people
D) 6 people, give or take 5 people

Question 19

Suppose that in a recent poll of 900 adults between the ages of 35 and 45, 22% surveyed said theyhave thought about participating in an extreme sport such as bungee jumping. Find the 95%confidence interval for the proportion of adults ages 35 to 45 who have thought about participatingin an extreme sport such as bungee jumping then choose the correct interpretation. (Round to thenearest tenth of a percent)

A)The population proportion of adults ages 35 to 45 who have thought about participating in anextreme sport such as bungee jumping is between 19.3% and 24.7%, with a confidence level of95%.
B)There is a 95% chance that the population of adults ages 35 to 45 who have thought aboutparticipating in an extreme sport such as bungee jumping is between 13.9% and 30.1%.
C)The population proportion of adults ages 35 to 45 who have thought about participating in anextreme sport such as bungee jumping is between 13.9% and 30.1%, with a confidence level of95%.

Question 20

Suppose that New Mexico lawmakers survey 160 randomly selected registered voters to see if theyfavor stricter laws regarding motorcycle helmet use for riders over the age of 17. The lawmakersbelieve the population proportion in favor of changing the law is 6% (based on historical data andprevious votes). Which of the following conditions for the Central Limit theorem arenotmet?

A)Relative to the population, the sample is not large enough.
B)The population proportion is too small and will not have enough expected successes.
C)The population proportion is too small and will not have enough expected failures.
D)None of these, all the conditions of the CLT are met.

Question 21

A polling agency wants to determine the size of a random sample needed to estimate theproportion of homeowners who keep a hand gun in their home for security. The estimate shouldhave margin of error no more than 2.5 percentage points at a 95% level of confidence. Choose themost conservative answer that is closest to your calculated number, rounding to the nearest wholeperson.

A) They should poll at least 1600 people.
B) They should poll at least 1200 people.
C) They should poll at least 400 people.
D) They should poll at least 1000 people.

Question 22

Which of the following statements is not true about a sampling distribution?

A) It is used for making inferences about a population.
B) It tells us how often we can expect to see particular values of our estimator.
C) It is the probability distribution of a statistic.
D) All these statements are true.

Question 23

Use the following information to answer the question. In a recent poll of 1200 randomly selected adult office workers, 32%
said they had worn a Halloween costume to the office at least once.

-What is the margin of error, using a 95% confidence level, for estimating the true populationproportion of adult office workers who have worn a Halloween costume to the office at least once?(Round to the nearest thousandth)

A) 0.026
B) 0.013
C) 0.158
D) 0.053

Question 24

Use the following information to answer the question. In a recent poll of 1200 randomly selected adult office workers, 32%said they had worn a Halloween costume to the office at least once.

-What is the standard error for the estimate of the proportion of all American adult office workers that have worn a Halloween costume to the office? Round to the nearest ten-thousandth.

A) 0.0135
B) 0.4672
C) 0.0143
D) 0.0002

Question 25

According to a snack cracker manufacturer, a batch of butter crackers has a defect rate of 8%. Suppose a quality inspector randomly inspects 500 crackers. Complete the following statement: The Quality inspector should expect
_{--------------------}defective crackers, give or take
_{--------------------}
Crackers.

A) 40; 16
B) 40; 6
C) 60; 16
D) 60; 12

Question 26

There are four colors in a bag containing 500 plastic chips. It is known that 28% of the chips are green. On average, how many chips from a random sample of 50 (with replacement) would be
Expected to be green?

A) 28
B) 14
C) 18
D) Not enough information to determine expected value.

Question 27

A random sample of 950 adult television viewers showed that 48% planned to watch sportingevent X. The margin of error is 4 percentage points with a 95% confidence. Does the confidenceinterval support the claim that the majority of adult television viewers plan to watch sporting eventX? Why?

A) Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 44% and 52%.
B) No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 46% and 50%.
C) No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 44% and 52%.
D) Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 46% and 50%.

Question 28

Use the following information to answer the question. A pescatarian is a person who eats fish and seafood but no otheranimal. An event planner does some research and finds that approximately 2.75% of the people in the area where a largeevent is to be held are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the localpopulation of about 150,000.

-Suppose the event planner assumes that 4% of the guests will be pescatarian so he orders 10 pescatarian meals. What is the approximate probability that more than 4% of the guests are
Pescatarian and that he will not have enough pescatarian meals? Round to the nearest thousandth.

A) 0.113
B) 0.470
C) 0.387
D) None of these

Question 29

Use the following information to answer the question. A pescatarian is a person who eats fish and seafood but no other animal. An event planner does some research and finds that approximately 2.75% of the people in the area where a large event is to be held are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the local population of about 150,000.

-Suppose the event planner assumes that only 1.6% of the guests will be pescatarian so he orders 4pescatarian meals. What is the approximate probability that he will havetoo manypescatarianmeals? Round to the nearest thousandth.

A) 0.387
B) 0.113
C) 0.613
D) 0.245

Question 30

Use the following information to answer the question. In a recent poll of 1100 randomly selected home delivery truck drivers,26% said they had encountered an aggressive dog on the job at least once.

-What is the margin of error, using a 95% confidence level, for estimating the true populationproportion of home delivery truck drivers who have encountered an aggressive dog on the job atleast once? (Round to the nearest thousandth)

A) 0.013
B) 0.053
C) 0.026
D) 0.004

Question 31

Researchers are interested in learning more about the age of women when they marry for the first time so they survey 500 married or divorced women and ask them how old they were when theyFirst married. The collection of the ages of the 500 women when they first
Married is a _{--------------------}.

A) Parameter
B) Sample
C) Statistic
D) Population

Question 32

If it is being used to make inferences about a population, a good statistic (or estimator) should

A) Show correlation.
B) Be derived from population data.
C) Be accurate and precise.
D) None of these.

Question 33

Suppose that in a recent poll of 1200 adults Suppose that in a recent poll of 1200 adults between the ages of 35 and 45, 38% surveyed said theyhave thought about getting elective plastic surgery. Find the 95% confidence interval for theproportion of adults ages 35 to 45 who have thought about getting elective plastic surgery thenchoose the correct interpretation. (Round to the nearest tenth of a percent)

A)The population proportion of adults ages 35 to 45 who have thought about getting electiveplastic surgery is between 35.2% and 40.7%, with a confidence level of 95%.
B)There is a 95% chance that the population of adults ages 35 to 45 who have thought aboutgetting elective plastic surgery is between 35.2% and 40.7%.
C)There is a 95% chance that the population of adults ages 35 to 45 who have thought aboutgetting elective plastic surgery is between 28.5% and 47.5%.
D)The population proportion of adults ages 35 to 45 who have thought about getting electiveplastic surgery is between 28.5% and 47.5%, with a confidence level of 95%.

Question 34

Fill in the blank to complete the statement.

-Suppose that the age of all the U. S. vice presidents when they took office was recorded. The collection of the ages of all the U. S. vice presidents when they took office is a .

A) Statistic
B) Sample
C) Population
D) Parameter

Question 35

Fill in the blank to complete the statement.

-Researchers are interested in learning more about the age of men when they marry for the first time so they survey 500 married or divorced men and ask them how old they were when they first
Married. The mean of age of the 500 men when they married for the first time would be a

A) Population
B) Parameter
C) Sample
D) Statistic

Question 36

Suppose that Illinois lawmakers survey 130 randomly selected registered voters to see if they favorcharging a deposit on aluminum cans to encourage recycling. The lawmakers believe thepopulation proportion in favor of changing the law is 93% (based on historical data and previousvotes). Which of the following conditions for the Central Limit theorem arenotmet?

A)Relative to the population, the sample is not large enough.
B)The population proportion is too small and will not have enough expected successes.
C)The population proportion is too small and will not have enough expected failures.
D)None of these, all the conditions of the CLT are met.

Question 37

Use the following information to answer the question. In a recent poll of 1100 randomly selected home delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once.

-What is the standard error for the estimate of the proportion of all home delivery truck drivers who have encountered an aggressive dog on the job at least once? Round to the nearest ten-thousandth.

A) 0.1322
B) 0.0002
C) 0.0132
D) 0.0141

Question 38

Use the following information to answer the question. A pollotarian is a person who eats poultry but no red meat. Awedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is tobe held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population ofabout 200,000.

-Suppose the wedding planner assumes that only 3% of the guests will be pollotarian so she orders 9pollotarian meals. What is the approximate probability that she will havetoo manypollotarianmeals? Round to the nearest thousandth.

A) 0.319
B) 0.251
C) 0.681
D) 0.477

Question 39

Max is interested in whether there is community interest in having local musicians perform musicin the park in the evenings during the summer. Max goes to the park for several evenings in a rowand asks people visiting the park whether they would like to hear music in the evening. Out of the200 people he surveys, 58% respond favorably. This scenario is describing what type of samplingbias?

A) Survey bias
B) Voluntary response bias
C) Nonresponse bias
D) Measurement bias

Question 40

Report the 95% confidence interval for the proportion of all adult office workers who have worn a Halloween costume to the office at least once. (Round final calculations to the nearest tenth of a
Percent)

A) (30.7%, 33.4%)
B) (29.4%, 34.6%)
C) (28.0%, 36.1%)
D) None of these

Question 41

Suppose that you and a friend read the following statement in a news report, "A recent pollfound that 54% of voters, give or take 3%, plan to vote for candidate X in the next election(with a confidence level of 95%)." Your friend then makes the statement, "Hey, look, there'sa 95% chance that somewhere between 51% and 57% of voters plan to vote for candidateX!" How would you explain to your friend why his statement is incorrect, be sure toprovide your friend with the correct interpretation of the confidence interval.

Question 42

Use the following information to answer the question. An event planner does some research and finds that in the area wherea large children's event is to be held, approximately 1.75% of the children are lactose intolerant. Treat the 250 childrenexpected at the event as a simple random sample from the local population of about 100,000 children.

-Suppose the event planner assumes that 2.8% of the children attending the event will belactose intolerant so he orders 7 lactose-free meals. What is the approximate probabilitythat more than 2.8% of the children attending the event are lactose intolerant and that he will not have enough lactose-free meals?
Round to the nearest thousandth.

Question 43

Can the way a survey question is asked affect the sample results?
Explain why such asample is or is not reflective of the population.

Question 44

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain25% "milky-white" marbles. Suppose that a bag containing 80 marbles is inspected.

-What value should we expect for our sampling percentage of milky-white marbles?
Howmany marbles would this be?
Round to the nearest whole marble.

Question 45

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain25% "milky-white" marbles. Suppose that a bag containing 80 marbles is inspected.

-Use your answers to fill in the blanks:
We expect_{--------------------} % milky-white marbles, give or take %_{--------------------}.

Question 46

Explain the difference between a population and a sample. Give an example of each.

Question 47

Frederick is interested in whether residents of his community are opposed to theconstruction of a party store on the corner of a busy intersection. He randomly polls 150residents in the community and receives responses from 55 residents. Of those whoresponded, 60% were opposed to the construction of the party store in the community soFrederick concludes that the majority of residents in his community oppose theconstruction of the party store. Explain what is wrong with this approach.

Question 48

Explain the difference between the standard error of a sample proportion and the marginof error of a confidence interval for a population proportion.

Question 49

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain25% "milky-white" marbles. Suppose that a bag containing 80 marbles is inspected.

-What is the margin of error, using a 95% confidence level, for estimating the trueproportion of adults who self-report that they cannot swim 24 yards?
Round to the nearest thousandth.

Question 50

Suppose that Michigan lawmakers survey 500 randomly selected registered voters to see ifthey favor an extension of the fall duck hunting season. The lawmakers believe thepopulation proportion in favor of extending the duck hunting season is 45% (based onhistorical data and previous votes). State the three conditions of the Central Limit Theoremand explain whether each condition is satisfied in this scenario.

Question 51

Use the following information to answer the question. An event planner does some research and finds that in the area where a large children's event is to be held, approximately 1.75% of the children are lactose intolerant. Treat the 250 children expected at the event as a simple random sample from the local population of about 100,000 children.

-On average, how many of the children attending the event would be expected to be lactoseintolerant, give or take how many?
Round to the nearest whole person.

Question 52

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain 25% "milky-white" marbles. Suppose that a bag containing 80 marbles is inspected.

-What is the standard error?
Round to the nearest tenth of a percent.

Question 53

Suppose a city manager conducts a poll and finds that a 95% confidence interval for theproportion of residents who support yard watering restrictions during extended periods ofno rain is 43% to 51%. Explain what the "95%" means.

Question 54

Use the following information to answer the question. A marble manufacturer advertises that its bags of marbles will contain25% "milky-white" marbles. Suppose that a bag containing 80 marbles is inspected.

-A survey of 800 randomly selected senior citizens showed that 55% said they planned towatch an upcoming political debate on television. The margin of error for the 95%confidence interval is 3.5 percentage points. Does the confidence interval support the claimthat the majority of senior citizens plan to watch the upcoming political debate ontelevision?
Explain why or why not.

Question 55

A sampling method should be as precise and accurate as possible. Explain what these twoterms mean and how each is measured.

Question 56

A polling agency wants to determine the size of the random sample needed to estimate theproportion of voters who favor proposal X. The estimate should have a margin of error nomore than 4.5 percentage points at a 95% level of confidence. Determine the minimum sizeof the sample, rounding to the nearest whole person.

Question 57

Explain the difference between a statistic and a parameter. Give an example of each.

Question 58

Use the following information to answer the question. In a recent poll of 900 randomly selected adults, 37% reported thatthey could not swim 24 yards (the length of a typical gymnasium lap pool).

-Report the 95% confidence interval for the proportion of adults who self-report that theycannot swim 24 yards. Round final calculations to the nearest tenth of a percent.

Question 59

Use the following information to answer the question. In a recent poll of 900 randomly selected adults, 37% reported thatthey could not swim 24 yards (the length of a typical gymnasium lap pool).

-What is the standard error for the estimate of the proportion of all adults that self-reportthat they cannot swim 24 yards?
Round to the nearest ten-thousandth.

Question 60

Suppose the event planner assumes that only 0.8% of the children attending the event willbe lactose intolerant so he orders 2 lactose-free meals. What is the approximate probability that he will have too many lactose-free meals?
Round to the nearest thousandth.