Deck 7: Sampling and Sampling Distributions

Question 1

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

Answer 1

True

Question 2

Cluster sampling is preferred when the objective is to increase precision.

Answer 2

False

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

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

Question 5

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 6

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

Question 7

Social-desirability bias refers to systematic difference between a group's "socially acceptable" responses to a survey or poll and this group's ultimate choice.

Question 8

We use a population parameter to make inferences about a sample statistic.

Question 9

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

Question 10

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 11

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 12

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

Question 13

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, se( ) = equivalently.

Question 14

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 15

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

Question 16

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

Question 17

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

Question 18

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.

Question 19

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

Question 20

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

Question 21

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

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

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

A) E( ) = E(X) = μ
B) E( ) = E(X) =
C) E( ) = E(X) =
D) E( ) = E(X) =

Question 24

A preferred approach to quality control is the ________ approach.

Question 25

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 26

According to the central limit theorem, the sampling distribution of approaches the normal distribution as the sample size ________.

Question 27

Which of the following meets the requirements of a cluster sample?

A) A population can be divided into 50 city blocks. The sample will include one hundred people who volunteer for the sample from any city block.
B) A population can be divided into 50 city blocks. The sample will include one hundred people chosen at random, without regard to the city block where they live.
C) A population can be divided into 50 city blocks. The sample will include all residents from two randomly chosen city blocks.
D) A population can be divided into 50 city blocks. The sample will include two people chosen at random from each city block.

Question 28

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 29

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 30

Cluster sampling is preferred when the objective is to ________.

Question 31

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 32

Which of the following is considered an estimate?

A) μ = 12
B) = 20
C) σ = 3.2
D) ^σ2 = 10

Question 33

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 34

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

Question 35

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

Question 36

The ________ of is the same as the mean of the individual observations.

Question 37

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 38

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 39

Which of the following is considered an estimator?

A)
B) µ
C) σ
D) ^σ2

Question 40

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 41

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 42

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 43

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

A) se( ) =
B) se( ) =
C) se( ) =
D) se( ) =

Question 44

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 45

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 46

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 47

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) 0.2525
B) 0.3707
C) 0.6293
D) 0.7486

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 between 25 and 30 school days is ________.

A) 0.0228
B) 0.0918
C) 0.8860
D) 0.9082

Question 49

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) 0.9088

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. What is the probability that in a one-game playoff, her score is more than 227?

A) 0.2676
B) 0.4389
C) 0.5596
D) 0.7324

Question 51

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) 0.1092
B) 0.4404
C) 0.5596
D) 0.8907

Question 52

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) 0.5889
B) 0.7486
C) 0.8413
D) 0.9048

Question 53

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 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

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 56

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 57

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) 0.7600
D) 0.8212

Question 58

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 59

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) 0.0620
B) 0.3520
C) 0.6480
D) 0.9382

Question 60

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 61

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 62

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) 0.8186
C) 0.8413
D) 0.8641

Question 63

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) 0.5047
C) 0.6591
D) 0.8130

Question 64

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students who receive an A is between 0.20 and 0.35 is

A) 0.1867.
B) 0.7776.
C) 0.8133.
D) 0.9633.

Question 65

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students that receive an A is 0.20 or less is ________.

A) 0.1855
B) 0.6266
C) 0.8133
D) 0.8900

Question 66

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) 0.1537
C) 0.3669
D) 0.8461

Question 67

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 68

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) 0.0478
C) 0.4763
D) 0.9525

Question 69

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) 0.9522

Question 70

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 71

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students who receive an A is not between 0.20 and 0.30 is ________.

A) 0.1867
B) 0.3711
C) 0.6266
D) 0.8133

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) 0.1926
C) 0.2005
D) 0.3936

Question 73

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) 0.3415
B) 0.4082
C) 0.6591
D) ≈1

Question 74

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) 0.1996
B) 0.7995
C) 0.8400
D) 0.9706

Question 75

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) 0.3836
D) 0.6179

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 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 78

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 79

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

A) np ≥ 5 and n(1 - p) ≤ 5
B) np ≤ 5 and n(1 - p) ≥ 5
C) np ≥ 5 and n(1 - p) ≥ 5
D) np ≤ 5 and n(1 - p) ≤ 5

Question 80

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. What are the expected value and the standard error for the proportion of students that receive an A?

A) 0.25 and 0.0031
B) 0.25 and 0.0559
C) 15.0 and 0.0031
D) 15.0 and 0.0559