Deck 7: Sampling and Sampling Distributions

Question 1

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.

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

If we had access to data that encompass the entire population,then the values of the parameters would be known and no statistical inference would be needed.

Answer 3

True

Question 4

A tutoring company claims that 75% of the high school students who hire one of their tutor's will improve their grades.

A)In a sample of 100 high school students,what is the probability that 80% or more improved their grades?
B)In a sample of 200 high school students,what is the probability that 80% or more improved their grades?
C)Comment on the reason for the difference between the computed probabilities in parts a and b.

Question 5

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

Question 6

In a recent investigation,the National Highway Traffic Safety Administration (NHTSA)found that the Chevrolet Volt and other electric vehicles do not pose a greater risk of fire than gasoline-powered vehicles (The Boston Globe,January 25,2012).Specifically,it was determined that "no discernible defect trend exists." Suppose a consumer advocacy group wants to verify some of these claims by constructing a

Question 7

A population consists of all items of interest in a statistical problem.

Question 8

For any population 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 .

Question 9

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 and .

Question 10

A sample consists of all items of interest in a statistical problem,whereas a population is a subset of the population.We calculate a parameter to make inferences about the unknown sample statistic.

Question 11

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

Question 12

A random sample of nine cast aluminum pots is taken from a production line once every hour.The interior diameter of the pots is measured and the sample mean is calculated.The target for the diameter is 12' and the standard deviation for the pot diameter is 0.05'.Assume the pot diameter is normally distributed.

A)Construct the centerline and the upper and lower control limits for the

Question 13

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

Question 14

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

Question 15

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

Question 16

We calculate a parameter to make inferences about a statistic.

Question 17

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

Question 18

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

Question 19

A large accounting firm gives out 1,000 job offers every year to new college graduates.Suppose that 85% of those that received offers accept the position.The following shows the number of graduates that have accepted jobs in the last four years.
Number of job offers accepted:

Question 20

A manufacturing process produces tubeless mountain bike tires in batches of 200.Past records show that 6% of the tires will not hold air.An engineer tests five batches,each one week apart,and shows the proportion of tires that will not hold air below.
Proportion of tires that will not hold air:

Question 21

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 22

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 23

Which of the following is considered an estimate?

A)
B)
C)
D)

Question 24

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 non-respondents

Question 25

A census is an example of __________.

A)Sample data
B)Sample statistic
C)Population data
D)Population parameter

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 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. Refer to Exhibit 7-1.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 27

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 28

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 29

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 ,the sampling distribution of the sample mean is normally distributed.
C)For a sample size ,the sampling distribution of the sample mean is normally distributed.
D)For a sample size

Question 30

Which of the following is not a population parameter?

A)
B)µ
C)σ
D)σ²

Question 31

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

A)
B)
C)
D)

Question 32

Which of the following is an example of a sample statistic?

A)
B)µ
C)σ
D)σ²

Question 33

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 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. Refer to Exhibit 7-1.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 34

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 non-respondents.

Question 35

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 non-respondents

Question 36

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

A)
B)
C)
D)

Question 37

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 38

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 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. Refer to Exhibit 7-1.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 39

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 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. Refer to Exhibit 7-1.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 40

Which of the following is considered an estimator?

A)
B)µ
C)σ
D)σ²

Question 41

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. Refer to Exhibit 7-3.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 42

Suppose that,on average,electricians earn approximately dollars per year in the United States.Assume that the distribution for electrician's yearly earnings is normally distributed and that the standard deviation is dollars. Refer to Exhibit 7-2.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 43

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 44

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. Refer to Exhibit 7-3.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 45

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. Refer to Exhibit 7-3.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 46

Suppose that,on average,electricians earn approximately dollars per year in the United States.Assume that the distribution for electrician's yearly earnings is normally distributed and that the standard deviation is dollars. Refer to Exhibit 7-2.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 dollars per year in the United States.Assume that the distribution for electrician's yearly earnings is normally distributed and that the standard deviation is dollars. Refer to Exhibit 7-2.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 48

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. Refer to Exhibit 7-4.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 49

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. Refer to Exhibit 7-4.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 50

A random sample of size 36 is taken from a population with mean and standard deviation . Refer to Exhibit 7-5.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 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. Refer to Exhibit 7-3.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 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
C)If the standard deviation of the population is known
D)Both A and B are correct

Question 53

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

A)
B)
C)
D)

Question 54

A random sample of size 36 is taken from a population with mean and standard deviation . Refer to Exhibit 7-5.The probability that the sample mean is greater than 18 is _______.

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

Question 55

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. Refer to Exhibit 7-4.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 56

A random sample of size 100 is taken from a population described by the proportion . Refer to Exhibit 7-6.What is the expected value and the standard deviation for the sampling distribution of the sample proportion?

A)Option A
B)Option B
C)Option C
D)Option D

Question 57

A random sample of size 36 is taken from a population with mean and standard deviation . Refer to Exhibit 7-5.What is the expected value and the standard deviation for the sampling distribution of the sample mean?

A)Option A
B)Option B
C)Option C
D)Option D

Question 58

Suppose that,on average,electricians earn approximately dollars per year in the United States.Assume that the distribution for electrician's yearly earnings is normally distributed and that the standard deviation is dollars. Refer to Exhibit 7-2.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 59

A random sample of size 36 is taken from a population with mean and standard deviation . Refer to Exhibit 7-5.The probability that the sample mean is less than 15 is ________.

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

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. Refer to Exhibit 7-4.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

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. Refer to Exhibit 7-10.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 62

The labor force participation rate is the number of people in the labor force divided by the number of people in the country that are of working age and not institutionalized.The BLS reported in February of 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. Refer to Exhibit 7-8.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 63

The labor force participation rate is the number of people in the labor force divided by the number of people in the country that are of working age and not institutionalized.The BLS reported in February of 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. Refer to Exhibit 7-8.What is the expected value and the standard deviation for a labor participation rate in the company's sample?

A)Option A
B)Option B
C)Option C
D)Option D

Question 64

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. Refer to Exhibit 7-9.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 65

A random sample of size 100 is taken from a population described by the proportion . Refer to Exhibit 7-6.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 66

Suppose 35% of homes in a Miami,Florida,neighborhood are under water (in other words,the amount due on the mortgage is larger than the value of the home).There are 160 homes in the neighborhood and 30 of those homes are owned by your friends.What is the probability that less than 30% of your friend's homes are under water?

A)0.2611
B)0.2843
C)0.6400
D)0.7389

Question 67

A random sample of size 100 is taken from a population described by the proportion . Refer to Exhibit 7-6.The probability that the sample proportion is greater than 0.62 is _______.

A)0.3409
B)0.4082
C)0.6591
D)

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. Refer to Exhibit 7-10.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 69

Successful firms must focus on the quality of the products and services that they offer.Which factor(s)contributes to the quest for quality?

A)Global competition
B)Consumer expectations
C)Technological advances
D)All of the above

Question 70

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. Refer to Exhibit 7-9.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 71

The labor force participation rate is the number of people in the labor force divided by the number of people in the country that are of working age and not institutionalized.The BLS reported in February of 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. Refer to Exhibit 7-8.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 72

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. Refer to Exhibit 7-10.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 73

The labor force participation rate is the number of people in the labor force divided by the number of people in the country that are of working age and not institutionalized.The BLS reported in February of 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. Refer to Exhibit 7-8.What is the probability that less than 60% of those surveyed are members of the labor force?

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

Question 74

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 ounces.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 75

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. Refer to Exhibit 7-9.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 76

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. Refer to Exhibit 7-10.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 77

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 78

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

A)
B)
C)
D)

Question 79

A random sample of size 100 is taken from a population described by the proportion . Refer to Exhibit 7-6.The probability that the sample proportion is less than 0.55 is ________.

A)
B)0.1539
C)0.3669
D)0.8461

Question 80

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. Refer to Exhibit 7-9.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