Deck 7: Sampling and Sampling Distributions

Question 1

For any population proportion p,the sampling distribution of will be approximately normal if the sample size n is sufficiently large.As a general guideline,the normal distribution approximation is justified when np ≥ 5 and n(1 −p)≥ 5.

Answer 1

True

Question 2

Stratified random sampling is preferred when the objective is to _______.

Answer 2

increase precision

Question 3

Selection bias occurs when the sample is mistakenly divided into strata,and random samples are drawn from each stratum.

Answer 3

False

Question 4

Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.

Question 5

In stratified random sampling,the population is first divided up into mutually exclusive and collectively exhaustive groups,called strata.A stratified sample includes randomly selected observations from each stratum,which are proportional to the stratum's size.

Question 6

If is normally distributed then we can transform it into a(n)_______ normal random variable.

Question 7

A parameter is a random variable,whereas a sample statistic is a constant.

Question 8

When a statistic is used to estimate a parameter,the statistic is referred to as an estimator.A particular value of the estimator is called an estimate.

Question 9

A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.

Question 10

A point estimator refers to an estimator that provides a single value.

Question 11

For any sample size n,the sampling distribution of is normal if the population from which the sample is drawn is uniformly distributed.

Question 12

The _______ _____ of is the same as the mean of the individual observations.

Question 13

For any population X with expected value µ and standard deviation σ,the sampling distribution of will be approximately normal if the sample size n is sufficiently small.As a general guideline,the normal distribution approximation is justified when n < 30.

Question 14

If the expected value of a sample mean equals the population mean,the sample mean is biased.

Question 15

The central limit theorem approximation improves as the sample size decreases.

Question 16

The standard deviation of suggests that the variation between observations is smaller than the variation between averages.

Question 17

The standard deviation of (standard error of the sample mean)equals the population standard deviation divided by the square root of the sample size,or, equivalently.

Question 18

For making statistical inferences,it is essential that the sampling distribution of is _________ distributed.

Question 19

Bias refers to the tendency of a sample statistic to systematically over- or underestimate a population parameter.

Question 20

Cluster sampling is preferred when the objective is to _______.

Question 21

Nonresponse bias occurs when _______.

A) the population has been divided into strata
B) portions of the population are excluded from the sample
C) cluster sampling is used instead of stratified random sampling
D) those responding to a survey or poll differ systematically from the nonrespondents

Question 22

Which of the following is not a form of bias?

A) Portions of the population are excluded from the sample.
B) Information from the sample is typical of information in the population.
C) Information from the sample overemphasizes a particular stratum of the population.
D) Those responding to a survey or poll differ systematically from the nonrespondents.

Question 23

Which of the following is considered an estimator?

A)
B) µ
C) σ
D) σ²

Question 24

Which of the following is true about statistics such as the sample mean or sample proportion?

A) A statistic is a constant.
B) A statistic is a parameter.
C) A statistic is always known.
D) A statistic is a random variable.

Question 25

Which of the following meets the requirements of a stratified random sample?

A) A population contains 10 members under the age of 25 and 20 members over the age of 25.The sample will include six people who volunteer for the sample.
B) A population contains 10 members under the age of 25 and 20 members over the age of 25.The sample will include six people chosen at random,without regard to age.
C) A population contains 10 members under the age of 25 and 20 members over the age of 25.The sample will include six males chosen at random,without regard to age.
D) A population contains 10 members under the age of 25 and 20 members over the age of 25.The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.

Question 26

Over the entire six years that students attend an Ohio elementary school,they are absent,on average,28 days due to influenza.Assume that the standard deviation over this time period is σ = 9 days.Upon graduation from elementary school,a random sample of 36 students is taken and asked how many days of school they missed due to influenza.What is the expected value for the sampling distribution of the number of school days missed due to influenza?

A) 6
B) 9
C) 28
D) 168

Question 27

Which of the following is considered an estimate?

A)
B)
C)
D)

Question 28

Bias can occur in sampling.Bias refers to _______.

A) the division of the population into overlapping groups
B) the creation of strata,which are proportional to the stratum's size
C) the use of cluster sampling instead of stratified random sampling
D) the tendency of a sample statistic to systematically over- or underestimate a population parameter

Question 29

Over the entire six years that students attend an Ohio elementary school,they are absent,on average,28 days due to influenza.Assume that the standard deviation over this time period is σ = 9 days.Upon graduation from elementary school,a random sample of 36 students is taken and asked how many days of school they missed due to influenza.What is the standard deviation for the sampling distribution of the number of school days missed due to influenza?

A) 1.22
B) 1.50
C) 2.25
D) 9.00

Question 30

According to the central limit theorem,the sampling distribution of approached the normal distribution as the sample size _______.

Question 31

Which of the following meets the requirements of a simple random sample?

A) A population contains 10 members under the age of 25 and 20 members over the age of 25.The sample will include six people who volunteer for the sample.
B) A population contains 10 members under the age of 25 and 20 members over the age of 25.The sample will include six people chosen at random,without regard to age.
C) A population contains 10 members under the age of 25 and 20 members over the age of 25.The sample will include six males chosen at random,without regard to age.
D) A population contains 10 members under the age of 25 and 20 members over the age of 25.The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.

Question 32

What is the relationship between the expected value of the sample mean and the expected value of the population?

A)
B)
C)
D)

Question 33

If a population is known to be normally distributed,what can be said of the sampling distribution of the sample mean drawn from this population?

A) For any sample size n,the sampling distribution of the sample mean is normally distributed.
B) For a sample size n < 50,the sampling distribution of the sample mean is normally distributed.
C) For a sample size n < 30,the sampling distribution of the sample mean is normally distributed.
D) For a sample size n > 30,the sampling distribution of the sample mean is normally distributed.

Question 34

A nursery sells trees of different types and heights.These trees average 60 inches in height with a standard deviation of 16 inches.Suppose that 75 pine trees are sold for planting at City Hall.What is the standard deviation for the sample mean?

A) 1.85
B) 3.41
C) 4
D) 16

Question 35

The _______ variation in the production process is caused by specific events or factors that can usually be identified and eliminated.

Question 36

A preferred approach to quality control is the _________ approach.

Question 37

What is the relationship between the standard deviation of the sample mean and the population standard deviation?

A)
B)
C)
D)

Question 38

Selection bias occurs when _______.

A) the population has been divided into strata
B) portions of the population are excluded from the consideration for the sample
C) cluster sampling is used instead of stratified random sampling
D) those responding to a survey or poll differ systematically from the nonrespondents

Question 39

Statistics are used to estimate population parameters,particularly when it is impossible or too expensive to poll an entire population.A particular value of a statistic is referred to as a(n)_______.

A) mean
B) stratum
C) estimate
D) finite correction factor

Question 40

How does the variance of the sample mean compare to the variance of the population?

A) It is smaller and therefore suggests that averages have less variation than individual observations.
B) It is larger and therefore suggests that averages have less variation than individual observations.
C) It is smaller and therefore suggests that averages have more variation than individual observations.
D) It is larger and therefore suggests that averages have more variation than individual observations.

Question 41

Suppose that,on average,electricians earn approximately µ = $54,000 per year in the United States.Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000.What is the probability that the average salary of four randomly selected electricians is less than $50,000?

A) 0.2514
B) 0.3707
C) 0.6293
D) 0.7486

Question 42

Over the entire six years that students attend an Ohio elementary school,they are absent,on average,28 days due to influenza.Assume that the standard deviation over this time period is σ = 9 days.Upon graduation from elementary school,a random sample of 36 students is taken and asked how many days of school they missed due to influenza.The probability that the sample mean is between 25 and 30 school days is _______.

A) 0.0228
B) 0.0918
C) 0.8854
D) 0.9082

Question 43

Susan has been on a bowling team for 14 years.After examining all of her scores over that period of time,she finds that they follow a normal distribution.Her average score is 225,with a standard deviation of 13.If during a typical month Susan bowls 64 games,what is the probability that her average score in this month is above 227?

A) 0.1093
B) 0.4404
C) 0.5596
D) 0.8907

Question 44

Suppose that,on average,electricians earn approximately µ = $54,000 per year in the United States.Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000.Given a sample of four electricians,what is the standard deviation for the sampling distribution of the sample mean?

A) 6,000
B) 12,000
C) 36,000
D) 54,000

Question 45

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6.The probability that the sample mean is less than 15 is _______.

A) 0.0228
B) 0.3707
C) 0.6293
D) 0.9772

Question 46

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years.After examining his records from the past 10 years,he finds that the scores have a mean of 76 and a standard deviation of 12.What is the probability Professor Elderman's class of 36 has a class average below 78?

A) 0.1587
B) 0.5675
C) 0.8413
D) Cannot be determined.

Question 47

The central limit theorem states that,for any distribution,as n gets larger,the sampling distribution of the sample mean _______.

A) becomes larger
B) becomes smaller
C) is closer to a normal distribution
D) is closer to the standard deviation

Question 48

Over the entire six years that students attend an Ohio elementary school,they are absent,on average,28 days due to influenza.Assume that the standard deviation over this time period is σ = 9 days.Upon graduation from elementary school,a random sample of 36 students is taken and asked how many days of school they missed due to influenza.The probability that the sample mean is less than 30 school days is _______.

A) 0.0918
B) 0.4129
C) 0.5871
D) 0.9082

Question 49

Susan has been on a bowling team for 14 years.After examining all of her scores over that period of time,she finds that they follow a normal distribution.Her average score is 225,with a standard deviation of 13.If during a typical week Susan bowls 16 games,what is the probability that her average score for the week is between 220 and 228?

A) 0.0618
B) 0.2390
C) 0.7594
D) 0.8212

Question 50

Susan has been on a bowling team for 14 years.After examining all of her scores over that period of time,she finds that they follow a normal distribution.Her average score is 225,with a standard deviation of 13.If during a typical week Susan bowls 16 games,what is the probability that her average score is more than 230?

A) 0.0618
B) 0.3520
C) 0.6480
D) 0.9382

Question 51

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years.After examining his records from the past 10 years,he finds that the scores have a mean of 76 and a standard deviation of 12.What is the probability that a class of 36 students will have an average greater than 70 on Professor Elderman's final exam?

A) 0.0014
B) 0.3085
C) 0.6915
D) 0.9986

Question 52

According to the central limit theorem,the distribution of the sample means is normal if _______.

A) the underlying population is normal
B) the sample size n ≥ 30
C) the standard deviation of the population is known
D) both the underlying population is normal and the sample size n ≥ 30 are correct

Question 53

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years.After examining his records from the past 10 years,he finds that the scores have a mean of 76 and a standard deviation of 12.Professor Elderman offers his class of 36 a pizza party if the class average is above 80.What is the probability that he will have to deliver on his promise?

A) 0.0228
B) 0.3707
C) 0.6293
D) 0.9772

Question 54

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years.After examining his records from the past 10 years,he finds that the scores have a mean of 76 and a standard deviation of 12.What is the probability that a class of 15 students will have a class average greater than 70 on Professor Elderman's final exam?

A) 0.0262
B) 0.6915
C) 0.9738
D) Cannot be determined.

Question 55

Suppose that,on average,electricians earn approximately µ = $54,000 per year in the United States.Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000.What is the probability that the average salary of four randomly selected electricians exceeds $60,000?

A) 0.1587
B) 0.3085
C) 0.6915
D) 0.8413

Question 56

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6.What are the expected value and the standard deviation for the sampling distribution of the sample mean?

A) 0.425 and 1.00
B) 0.425 and 2.83
C) 17 and 1.00
D) 17 and 2.83

Question 57

Suppose that,on average,electricians earn approximately µ = $54,000 per year in the United States.Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000 dollars.What is the probability that the average salary of four randomly selected electricians is more than $50,000 but less than $60,000?

A) 0.5899
B) 0.7486
C) 0.8413
D) 0.9048

Question 58

Susan has been on a bowling team for 14 years.After examining all of her scores over that period of time,she finds that they follow a normal distribution.Her average score is 225,with a standard deviation of 13.What is the probability that in a one-game playoff,her score is more than 227?

A) 0.2676
B) 0.4404
C) 0.5596
D) 0.7324

Question 59

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6.The probability that the sample mean is greater than 18 is _______.

A) 0.1587
B) 0.4325
C) 0.5675
D) 0.8413

Question 60

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6.The probability that the sample mean is between 15 and 18 is _______.

A) 0.0228
B) 0.8185
C) 0.8413
D) 0.8641

Question 61

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis.Due to a decade-long rivalry between the Patriots and the city's own team,the Colts,most Indianapolis residents were rooting heartily for the Giants.Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots.What is the probability that,of a sample of 100 Indianapolis residents,at least 15% were rooting for the Patriots in Super Bowl XLVI?

A) 0.0300
B) 0.0475
C) 0.4763
D) 0.9525

Question 62

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com).A marketing company asks 120 working-age people if they either have a job or are looking for a job,or,in other words,whether they are in the labor force.What is the probability that fewer than 60% of those surveyed are members of the labor force?

A) 0.2005
B) 0.7995
C) 0.8400
D) 0.9706

Question 63

A local company makes snack-size bags of potato chips.Each day,the company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips.However,due to imperfect technology,the actual amount placed in a given bag varies.Assume the amount placed in each of the 400 bags is normally distributed and has a standard deviation of 0.1 ounce.What is the probability that a sample of 40 bags has an average weight of at least 2.02 ounces?

A) 0.0150
B) 0.0918
C) 0.1038
D) 0.4207

Question 64

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com).A marketing company asks 120 working-age people if they either have a job or are looking for a job,or,in other words,whether they are in the labor force.For the company's sample,the probability that the proportion of people who are in the labor force is greater than 0.65 is _______.

A) 0.1179
B) 0.3000
C) 0.3821
D) 0.6179

Question 65

According to the 2011 Gallup daily tracking polls (www.gallup.com,February 3,2012),Mississippi is the most conservative U.S.state,with 53.4 percent of its residents identifying themselves as conservative.What is the probability that fewer than 45 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative?

A) 0.0499
B) 0.1873
C) 0.3745
D) 0.6255

Question 66

According to the 2011 Gallup daily tracking polls (www.gallup.com,February 3,2012),Mississippi is the most conservative U.S.state,with 53.4 percent of its residents identifying themselves as conservative.What is the probability that at least 100 but fewer than 115 respondents of a random sample of 200 Mississippi residents identify as conservative?

A) 0.1685
B) 0.3370
C) 0.7085
D) 0.8770

Question 67

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis.Due to a decade-long rivalry between the Patriots and the city's own team,the Colts,most Indianapolis residents were rooting heartily for the Giants.Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots.What is the probability that from a sample of 200 Indianapolis residents,fewer than 170 were rooting for the Giants in Super Bowl XLIV?

A) 0.0091
B) 0.0212
C) 0.4954
D) 0.9908

Question 68

According to the 2011 Gallup daily tracking polls (www.gallup.com,February 3,2012),Mississippi is the most conservative U.S.state,with 53.4 percent of its residents identifying themselves as conservative.What is the probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative?

A) 0.0499
B) 0.2483
C) 0.4966
D) 0.7517

Question 69

Using the central limit theorem,applied to the sampling distribution of the sample proportion,what conditions must be met?

A) and
B) and
C) and
D)

Question 70

A random sample of size 100 is taken from a population described by the proportion p = 0.60.The probability that the sample proportion is less than 0.55 is _______.

A) ≈ 0
B) 0.1539
C) 0.3669
D) 0.8461

Question 71

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis.Due to a decade-long rivalry between the Patriots and the city's own team,the Colts,most Indianapolis residents were rooting heartily for the Giants.Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots.What is the probability that from a sample of 40 Indianapolis residents,fewer than 95% were rooting for the Giants in Super Bowl XLIV?

A) 0.0474
B) 0.1469
C) 0.8531
D) Cannot be determined

Question 72

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com).A marketing company asks 120 working-age people if they either have a job or are looking for a job,or,in other words,whether they are in the labor force.What is the probability that between 60% and 62.5% of those surveyed are members of the labor force?

A) 0.0243
B) 0.1931
C) 0.2005
D) 0.3936

Question 73

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com).A marketing company asks 120 working-age people if they either have a job or are looking for a job,or,in other words,whether they are in the labor force.What are the expected value and the standard error for a labor participation rate in the company's sample?

A) 0.637 and 0.0019
B) 0.637 and 0.0439
C) 76.44 and 0.0019
D) 76.44 and 0.0439

Question 74

A random sample of size 100 is taken from a population described by the proportion p = 0.60.The probability that the sample proportion is between 0.55 and 0.62 is _______.

A) 0.1539
B) 0.5052
C) 0.6591
D) 0.8130

Question 75

According to the 2011 Gallup daily tracking polls (www.gallup.com,February 3,2012),Mississippi is the most conservative U.S.state,with 53.4 percent of its residents identifying themselves as conservative.What is the probability that at least 60% of a random sample of 200 Mississippi residents identify themselves as conservative?

A) 0.0307
B) 0.3530
C) 0.4847
D) 0.9693

Question 76

A random sample of size 100 is taken from a population described by the proportion p = 0.60.What are the expected value and the standard error for the sampling distribution of the sample proportion?

A) 0.006 and 0.0024
B) 0.060 and 0.049
C) 0.600 and 0.0024
D) 0.600 and 0.049

Question 77

A random sample of size 100 is taken from a population described by the proportion p = 0.60.The probability that the sample proportion is greater than 0.62 is _______.

A) 0.3409
B) 0.4082
C) 0.6591
D)

Question 78

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis.Due to a decade-long rivalry between the Patriots and the city's own team,the Colts,most Indianapolis residents were rooting heartily for the Giants.Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots.What is the probability that from a sample of 100 Indianapolis residents,fewer than 95% were rooting for the Giants in Super Bowl XLVI?

A) 0.0300
B) 0.0475
C) 0.4763
D) 0.9525

Question 79

The finite correction factor is always _______.

A) less than one,and therefore increases the standard deviations of and computed under the assumption of infinite population
B) less than one,and therefore decreases the standard deviations of and computed under the assumption of infinite population
C) greater than one,and therefore increases the standard deviations of and computed under the assumption of infinite population
D) greater than one,and therefore decreases the standard deviations of

Question 80

Under what condition is the finite population correction factor used for computing the standard error of and ?

A) n ≥ Np
B) n < Np
C) n ≥ 0.05N
D) n < 0.05N