Deck 7: Sampling and Sampling Distributions

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Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.
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Cluster sampling is preferred when the objective is to increase precision.
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Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.
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The central limit theorem approximation improves as the sample size decreases.
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For any population X with expected value µ and standard deviation σ, the sampling distribution of 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.<div style=padding-top: 35px> 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.
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If the expected value of a sample mean equals the population mean, the sample mean is biased.
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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.
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We use a population parameter to make inferences about a sample statistic.
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Stratified random sampling is preferred when the objective is to ________.
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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.
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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.
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The standard deviation of The standard deviation of   suggests that the variation between observations is smaller than the variation between averages.<div style=padding-top: 35px> suggests that the variation between observations is smaller than the variation between averages.
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The standard deviation of 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.<div style=padding-top: 35px> (standard error of the sample mean) equals the population standard deviation divided by the square root of the sample size, or, se( 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.<div style=padding-top: 35px> ) = 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.<div style=padding-top: 35px> equivalently.
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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.
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A point estimator refers to an estimator that provides a single value.
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Bias refers to the tendency of a sample statistic to systematically over-or underestimate a population parameter.
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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.
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For any population proportion p, the sampling distribution of 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.<div style=padding-top: 35px> 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.
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A parameter is a random variable, whereas a sample statistic is a constant.
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For any sample size n, the sampling distribution of For any sample size n, the sampling distribution of   is normal if the population from which the sample is drawn is uniformly distributed.<div style=padding-top: 35px> is normal if the population from which the sample is drawn is uniformly distributed.
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If If   is normally distributed then we can transform it into a(n) ________ normal random variable. <div style=padding-top: 35px> is normally distributed then we can transform it into a(n) ________ normal random variable.
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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
What is the relationship between the expected value of the sample mean and the expected value of the population?

A) E( <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   <div style=padding-top: 35px> ) = E(X) = μ
B) E( <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   <div style=padding-top: 35px> ) = E(X) = <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   <div style=padding-top: 35px>
C) E( <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   <div style=padding-top: 35px> ) = E(X) = <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   <div style=padding-top: 35px>
D) E( <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   <div style=padding-top: 35px> ) = E(X) = <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   <div style=padding-top: 35px>
Question
A preferred approach to quality control is the ________ approach.
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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
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According to the central limit theorem, the sampling distribution of According to the central limit theorem, the sampling distribution of   approaches the normal distribution as the sample size ________. <div style=padding-top: 35px> approaches the normal distribution as the sample size ________.
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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.
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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
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
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Cluster sampling is preferred when the objective is to ________.
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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
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Which of the following is considered an estimate?

A) μ = 12
B) <strong>Which of the following is considered an estimate?</strong> A) μ = 12 B)   = 20 C) σ = 3.2 D) <sup>σ</sup><sup>2</sup> = 10 <div style=padding-top: 35px> = 20
C) σ = 3.2
D) σ2 = 10
Question
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.
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For making statistical inferences, it is essential that the sampling distribution of For making statistical inferences, it is essential that the sampling distribution of   is ________ distributed. <div style=padding-top: 35px> is ________ distributed.
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The ________ variation in the production process is caused by specific events or factors that can usually be identified and eliminated.
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The ________ of The ________ of   is the same as the mean of the individual observations. <div style=padding-top: 35px> is the same as the mean of the individual observations.
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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.
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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
Which of the following is considered an estimator?

A) <strong>Which of the following is considered an estimator?</strong> A)   B) µ C) σ D) <sup>σ</sup><sup>2</sup> <sup <div style=padding-top: 35px>
B) µ
C) σ
D) σ2
Question
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
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
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
What is the relationship between the standard deviation of the sample mean and the population standard deviation?

A) se( <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   <div style=padding-top: 35px> ) = <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   <div style=padding-top: 35px>
B) se( <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   <div style=padding-top: 35px> ) = <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   <div style=padding-top: 35px>
C) se( <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   <div style=padding-top: 35px> ) = <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   <div style=padding-top: 35px>
D) se( <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   <div style=padding-top: 35px> ) = <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   <div style=padding-top: 35px>
Question
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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Deck 7: Sampling and Sampling Distributions
1
Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.
True
2
Cluster sampling is preferred when the objective is to increase precision.
False
3
Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.
False
4
The central limit theorem approximation improves as the sample size decreases.
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5
For any population X with expected value µ and standard deviation σ, the sampling distribution of 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. 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.
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6
If the expected value of a sample mean equals the population mean, the sample mean is biased.
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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.
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8
We use a population parameter to make inferences about a sample statistic.
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9
Stratified random sampling is preferred when the objective is to ________.
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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.
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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.
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12
The standard deviation of The standard deviation of   suggests that the variation between observations is smaller than the variation between averages. suggests that the variation between observations is smaller than the variation between averages.
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13
The standard deviation of 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. (standard error of the sample mean) equals the population standard deviation divided by the square root of the sample size, or, se( 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. ) = 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. equivalently.
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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.
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15
A point estimator refers to an estimator that provides a single value.
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16
Bias refers to the tendency of a sample statistic to systematically over-or underestimate a population parameter.
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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.
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18
For any population proportion p, the sampling distribution of 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. 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.
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19
A parameter is a random variable, whereas a sample statistic is a constant.
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20
For any sample size n, the sampling distribution of For any sample size n, the sampling distribution of   is normal if the population from which the sample is drawn is uniformly distributed. is normal if the population from which the sample is drawn is uniformly distributed.
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21
If If   is normally distributed then we can transform it into a(n) ________ normal random variable. is normally distributed then we can transform it into a(n) ________ normal random variable.
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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.
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23
What is the relationship between the expected value of the sample mean and the expected value of the population?

A) E( <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   ) = E(X) = μ
B) E( <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   ) = E(X) = <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =
C) E( <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   ) = E(X) = <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =
D) E( <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =   ) = E(X) = <strong>What is the relationship between the expected value of the sample mean and the expected value of the population?</strong> A) E(   ) = E(X) = μ B) E(   ) = E(X) =   C) E(   ) = E(X) =   D) E(   ) = E(X) =
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24
A preferred approach to quality control is the ________ approach.
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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
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26
According to the central limit theorem, the sampling distribution of According to the central limit theorem, the sampling distribution of   approaches the normal distribution as the sample size ________. approaches the normal distribution as the sample size ________.
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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.
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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.
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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
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30
Cluster sampling is preferred when the objective is to ________.
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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
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32
Which of the following is considered an estimate?

A) μ = 12
B) <strong>Which of the following is considered an estimate?</strong> A) μ = 12 B)   = 20 C) σ = 3.2 D) <sup>σ</sup><sup>2</sup> = 10 = 20
C) σ = 3.2
D) σ2 = 10
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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.
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34
For making statistical inferences, it is essential that the sampling distribution of For making statistical inferences, it is essential that the sampling distribution of   is ________ distributed. is ________ distributed.
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35
The ________ variation in the production process is caused by specific events or factors that can usually be identified and eliminated.
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36
The ________ of The ________ of   is the same as the mean of the individual observations. is the same as the mean of the individual observations.
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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.
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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.
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39
Which of the following is considered an estimator?

A) <strong>Which of the following is considered an estimator?</strong> A)   B) µ C) σ D) <sup>σ</sup><sup>2</sup> <sup
B) µ
C) σ
D) σ2
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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
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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
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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
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43
What is the relationship between the standard deviation of the sample mean and the population standard deviation?

A) se( <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   ) = <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =
B) se( <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   ) = <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =
C) se( <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   ) = <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =
D) se( <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =   ) = <strong>What is the relationship between the standard deviation of the sample mean and the population standard deviation?</strong> A) se(   ) =   B) se(   ) =   C) se(   ) =   D) se(   ) =
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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
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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
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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
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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
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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.
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Unlock Deck
Unlock for access to all 136 flashcards in this deck.