Deck 7: Sampling and Sampling Distributions

Question 1

The standard deviation of a sampling distribution of the sample means is commonly called the standard error of the mean.

Answer 1

True

Question 2

Saving time and money are reasons to take a sample rather than do a census.

Answer 2

True

Question 3

With cluster sampling,there is homogeneity within a subgroup or stratum.

Answer 3

False

Question 4

The two major categories of sampling methods are proportionate and disproportionate sampling.

Question 5

A nonrandom sampling technique which is similar to stratified random sampling is called quota sampling.

Question 6

The directory or map from which a sample is taken is called the frame.

Question 7

Contrast sampling to census and differentiate among different methods of sampling,which include simple,stratified,systematic,and cluster random sampling;and convenience,judgment,quota,and snowball nonrandom sampling,by assessing the advantages associated with each.

Question 8

A population list,map,directory,or other source used to represent the population from which a sample is taken is called the census.

Question 9

Cluster (or area)sampling is a type of random sampling technique.

Question 10

In a random sampling technique every unit of the population has a randomly varying chance or probability of being included in the sample.

Question 11

A major limitation of nonrandom samples is that they are not appropriate for most statistical methods.

Question 12

The central limit theorem states that if the sample size,n,is large enough (n ≥30),the distribution of the sample means is uniformly distributed regardless of the shape of the population.

Question 13

If every unit of the population has the same probability of being selected to the sample,then the researcher is conducting random sampling.

Question 14

If a researcher selects every k^th item from a population of N items,then she is likely conducting a stratified random sampling.

Question 15

Nonsampling error occurs when,due to chance,the sample is not representative of the population.

Question 16

Describe the distribution of a sample's proportion using the z formula for sample proportions.

Question 17

In some situations sampling may be the only option because the population is inaccessible.

Question 18

A sampling distribution is the distribution of a sample statistic such as the sample mean or sample proportion.

Question 19

Describe the distribution of a sample's mean using the central limit theorem,correcting for a finite population if necessary.

Question 20

Systematic sampling is a type of nonrandom sampling technique.

Question 21

Abel Alonzo,Director of Human Resources,is exploring employee absenteeism at the Harrison Haulers Plant.Abel knows that absenteeism varies significantly between departments.For example,workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers.He orders a random sample of 10% of the workers from each of the six departments.Abel' sample is a ___.

A)proportionate systematic sample
B)proportionate stratified sample
C)disproportionate systematic sample
D)disproportionate stratified sample
E)proportionate cluster sample

Question 22

A carload of steel rods has arrived at Cybermatic Construction Company.The car contains 1,000 bundles of 50 rods each.Claude Ong,manager of Quality Assurance,directs the receiving crew to deliver the 63rd and 458th bundles to his crew for 100% inspection.Claude randomly selected 63 and 458 from a table of random numbers.Claude's sample of 100 rods is a ___.

A)cluster sample
B)simple random sample
C)quota sample
D)systematic sample
E)stratified sample

Question 23

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system.She knows that 2,500 payroll vouchers have been issued since January 1,2000,and her staff doesn't have time to inspect each voucher.So,she orders her staff to inspect the last 200 vouchers.Her sample is a ___.

A)stratified sample
B)simple random sample
C)convenience sample
D)systematic sample
E)cluster sample

Question 24

A carload of palletized aluminum castings has arrived at Mansfield Motor Manufacturers.The car contains 1,000 pallets of 100 castings each.Mario Munoz,manager of Quality Assurance,directs the receiving crew to deliver the 127th and 869th pallets to his crew for 100% inspection.Mario randomly selected 127 and 869 from a table of random numbers.Mario's sample of 200 castings is a ___.

A)simple random sample
B)systematic sample
C)stratified sample
D)cluster sample
E)convenience sample

Question 25

Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers.Accordingly,he plans a sample of waiting times for walk-in customers.Albert randomly selects 4 as a starting point and instructs his staff to record the waiting times for the 4th walk-in customer and every 10th customer thereafter (4,14,24,etc. ).Albert's sample is a ___.

A)simple random sample
B)cluster sample
C)convenience sample
D)stratified sample
E)systematic sample

Question 26

Kristen Ashford purchased the subscribers list for Wind Surfing magazine.She plans to survey a sample of the subscribers before using the list in her mail order business.She randomly selects the fourth name as a starting point and then selects every 50th subsequent name (54,104,154,etc. ).Her sample is a ___.

A)simple random sample
B)stratified sample
C)systematic sample
D)convenience sample
E)cluster sample

Question 27

On Saturdays,cars arrive at David Zebda's Scrub and Shine Car Wash at the rate of 80 cars per hour during the ten-hour shift.David wants a sample of 40 Saturday customers to answer the long version of his quality service questionnaire.He randomly selects 9 as a starting point and instructs the crew to select the 9th customer and each customer at intervals of 20 (9,29,49,etc. ).His sample is a ___.

A)convenience sample
B)simple random sample
C)unsystematic sample
D)stratified sample
E)systematic sample

Question 28

Financial analyst Larry Potts needs a sample of 100 securities listed on the Toronto Stock Exchange.In the current issue of the Report on Business Magazine,2,531 securities are listed in the "Toronto Exchange Composite Transactions," an alphabetical listing of all securities traded on the previous business day.Larry randomly selects the 7th security as a starting point,and selects every 25th security thereafter (7,32,57,etc. ).His sample is a ___.

A)quota sample
B)simple random sample
C)stratified sample
D)systematic sample
E)cluster sample

Question 29

Kristen Ashford purchased the subscribers list for Wind Surfing magazine.She plans to survey a sample of the subscribers before using the list in her mail order business.The names are numbered consecutively from 1 to 5,000.Kristen chooses her sample by selecting four-digit numbers (1 to 5,000)from a random number table.Her sample is a ___.

A)simple random sample
B)stratified sample
C)systematic sample
D)convenience sample
E)cluster sample

Question 30

Catherine Chao,Director of Marketing Research,needs a sample of households to participate in the testing of a new toothpaste package.She directs the seven members of her staff to find five households each.Catherine's sample is a ___.

A)cluster sample
B)proportionate stratified sample
C)quota sample
D)disproportionate stratified sample
E)simple random sample

Question 31

Abel Alonzo,Director of Human Resources,is exploring employee absenteeism at the Harrison Haulers Plant.Abel knows that absenteeism varies significantly between departments.For example,workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers.He orders a random sample of 10 workers from each of the six departments.Abel' sample is a ___.

A)proportionate systematic sample
B)proportionate stratified sample
C)disproportionate systematic sample
D)disproportionate stratified sample
E)proportionate cluster sample

Question 32

Increasing the sample size causes the numerical value of the standard error of the mean to increase.

Question 33

On Saturdays,cars arrive at David Zebda's Scrub and Shine Car Wash at the rate of 80 cars per hour during the ten-hour shift.David wants a sample of 40 Saturday customers to answer the long version of his quality service questionnaire.He instructs the Saturday crew to select the first 40 customers.His sample is a ___.

A)convenience sample
B)simple random sample
C)systematic sample
D)stratified sample
E)cluster sample

Question 34

Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers.Accordingly,he plans a sample of waiting times for walk-in customers.Albert instructs his staff to record the waiting times for the first 45 walk-in customers arriving after the noon hour.Albert's sample is a ___.

A)simple random sample
B)systematic sample
C)convenience sample
D)stratified sample
E)cluster sample

Question 35

Financial analyst Larry Potts needs a sample of 100 securities listed on either the Toronto Stock Exchange (TSX)or the New York Stock Exchange (NYSE).According to the Report on Business Magazine's "Stock Market Data Bank," 2,531 TSX securities and 746 NYSE securities were traded on the previous business day.Larry directs his staff to randomly select 77 TSX and 23 NYSE securities.His sample is a ___.

A)disproportionate systematic sample
B)disproportionate stratified sample
C)proportionate stratified sample
D)proportionate systematic sample
E)proportionate cluster sampling

Question 36

Kristen Ashford purchased the subscribers list for Wind Surfing magazine.She plans to survey a sample of the subscribers before using the list in her mail order business.She chooses the first 100 of the 5,000 names.Her sample is a ___.

A)simple random sample
B)stratified sample
C)systematic sample
D)convenience sample
E)cluster sample

Question 37

Financial analyst Larry Potts needs a sample of 100 securities listed on the Toronto Stock Exchange.In the current issue of the Report on Business Magazine,2,531 securities are listed in the "Toronto Exchange Composite Transactions," an alphabetical listing of all securities traded on the previous business day.Larry uses a table of random numbers to select 100 numbers between 1 and 2,531.His sample is a ___.

A)quota sample
B)simple random sample
C)systematic sample
D)stratified sample
E)cluster sample

Question 38

Catherine Chao,Director of Marketing Research,needs a sample of households to participate in the testing of a new toothpaste package.She chooses thirty-six of her closest friends.Catherine's sample is a ___.

A)cluster sample
B)convenience sample
C)quota sample
D)systematic sample
E)random sample

Question 39

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system.She knows that 2,500 payroll vouchers have been issued since January 1,2000,and her staff doesn't have time to inspect each voucher.So,she randomly selects 53 as a starting point and orders her staff to inspect the 53rd voucher and each voucher at an increment of 100 (53,153,253,etc. ).Her sample is a ___.

A)stratified sample
B)simple random sample
C)convenience sample
D)cluster sample
E)systematic sample

Question 40

According to the central limit theorem,if a sample of size 100 is drawn from a population with a mean of 80,the mean of all sample means would equal ___.

A)0.80
B)8
C)80
D)100
E)120

Question 41

Suppose a population has a mean of 870 and a variance of 1,600.If a random sample is size 64 is drawn from the population,the probability that the sample mean is between 860 and 875 is ___.

A)0.9544
B)0.6826
C)0.8785
D)0.5899
E)0.8185

Question 42

Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers.Accordingly,he plans a sample of waiting times for walk-in customers.If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,the probability that Albert's sample of 64 will have a mean less than 14 minutes is ___.

A)0.4772
B)0.0228
C)0.9772
D)0.9544
E)1.0000

Question 43

According to the central limit theorem,for samples of size 169 drawn from a population with µ = 1,014 and σ = 65,the mean of the sampling distribution of sample means would equal ___.

A)1,014
B)65
C)5
D)6
E)3

Question 44

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean of more than 404.5 is ___.

A)0.0139
B)0.4861
C)0.4878
D)0.0122
E)0.5000

Question 45

According to the central limit theorem,for samples of size 169 drawn from a population with µ = 1,014 and σ = 65,the standard deviation of the sampling distribution of sample means would equal ___.

A)1,014
B)65
C)15
D)6
E)5

Question 46

According to the central limit theorem,for samples of size 64 drawn from a population with µ = 800 and σ = 56,the mean of the sampling distribution of sample means would equal ___.

A)7
B)8
C)100
D)800
E)80

Question 47

According to the central limit theorem,if a sample of size 64 is drawn from a population with a mean of 56,the mean of all sample means would equal ___.

A)7.00
B)56.00
C)64.00
D)0.875
E)128.00

Question 48

According to the central limit theorem,if a sample of size 81 is drawn from a population with a standard deviation of 72,the standard deviation of the distribution of the sample means would equal ___.

A)8
B)9
C)7.2
D)0.875
E)128.00

Question 49

Suppose a population has a mean of 90 and a standard deviation of 28.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean of more than 95 is ___.

A)0.1056
B)0.3944
C)0.4286
D)0.8944
E)1.0000

Question 50

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean less than 402 is ___.

A)0.3413
B)0.6826
C)0.8413
D)0.1587
E)0.9875

Question 51

Increasing the sample size causes the sampling distribution of to ___.

A)shift to the right
B)shift to the left
C)have more dispersion
D)have less dispersion
E)stay unchanged

Question 52

Suppose a population has a mean of 870 and a variance of 8,100.If a random sample is size 36 is drawn from the population,the probability that the sample mean is between 840 and 900 is ___.

A)0.9544
B)0.6826
C)0.8185
D)0.5899
E)0.0897

Question 53

According to the central limit theorem,if a sample of size 100 is drawn from a population with a standard deviation of 80,the standard deviation of sample means would equal ___.

A)0.80
B)8
C)80
D)800
E)0.080

Question 54

Suppose a population has a mean of 90 and a standard deviation of 28.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean between 80 and 100 is ___.

A)0.9876
B)0.0124
C)0.4938
D)0.0062
E)1.0000

Question 55

According to the central limit theorem,for samples of size 64 drawn from a population with µ = 800 and σ = 56,the standard deviation of the sampling distribution of sample means would equal ___.

A)7
B)8
C)100
D)800
E)80

Question 56

Suppose a population has a mean of 450 and a variance of 900.If a random sample is size 100 is drawn from the population,the probability that the sample mean is between 448 and 453 is ___.

A)0.4972
B)0.6826
C)0.4101
D)0.5899
E)0.9878

Question 57

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean between 395.5 and 404.5 is ___.

A)0.9756
B)0.0244
C)0.0278
D)0.9722
E)1.0000

Question 58

Suppose a population has a mean of 90 and a standard deviation of 28.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean between 85 and 95 is ___.

A)0.1056
B)0.3944
C)0.7888
D)0.2112
E)0.5000

Question 59

Suppose a population has a mean of 90 and a standard deviation of 28.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean of less than 84 is ___.

A)0.9332
B)0.0668
C)0.4332
D)0.8664
E)1.0000

Question 60

According to the central limit theorem,if a sample of size 64 is drawn from a population with a standard deviation of 80,the standard deviation of sample means would equal ___.

A)10.000
B)1.250
C)0.125
D)0.800
E)0.080

Question 61

If the population proportion is 0.90 and a sample of size 64 is taken,what is the probability that the sample proportion is more than 0.89?

A)0.1064
B)0.2700
C)0.3936
D)0.6064
E)0.9000

Question 62

Suppose 30% of a population possess a given characteristic.If a random sample of size 1200 is drawn from the population,then the probability that less than 348 possess that characteristic is ___.

A)0.2236
B)0.2764
C)0.2900
D)0.7764
E)0.3336

Question 63

A carload of steel rods has arrived at Cybermatic Construction Company.The car contains 50,000 rods.Claude Ong,manager of Quality Assurance,directs his crew measure the lengths of 100 randomly selected rods.If the population of rods have a mean length of 120 centimetres and a standard deviation of 0.05 centimetres,the probability that Claude's sample has a mean less than 119.985 centimetres is ___.

A)0.9974
B)0.0026
C)0.4987
D)0.0013
E)0.0030

Question 64

Catherine Chao,Director of Marketing Research,needs a sample of Ottawa households to participate in the testing of a new toothpaste package.If 40% of the households in Ottawa prefer the new package,the probability that Catherine's random sample of 300 households will have a sample proportion greater than 0.45 is ___.

A)0.9232
B)0.0768
C)0.4616
D)0.0384
E)0.8974

Question 65

Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers.Accordingly,he plans a sample of waiting times for walk-in customers.If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,the probability that Albert's sample of 64 will have a mean less than 15 minutes is ___.

A)0.5000
B)0.0228
C)0.9072
D)0.9544
E)1.0000

Question 66

Suppose 40% of all seniors have a computer at home and a sample of 100 is taken.What is the probability that more than 50 of those in the sample have a computer at home?

A)0.4793
B)0.9793
C)0.0207
D)0.5207
E)0.6754

Question 67

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system.If 10% of the 5,000 payroll vouchers issued since January 1,2000,have irregularities,the probability that Pinky's random sample of 200 vouchers will have a sample proportion greater than .06 is ___.

A)0.4706
B)0.9706
C)0.0588
D)0.9412
E)0.9876

Question 68

Suppose 40% of the population possess a given characteristic.If a random sample of size 300 is drawn from the population,then the probability that 44% or fewer of the samples possess the characteristic is ___.

A)0.0793
B)0.4207
C)0.9207
D)0.9900
E)1.0000

Question 69

If the population proportion is 0.90 and a sample of size 64 is taken,what is the probability that the sample proportion is less than 0.88?

A)0.2019
B)0.2981
C)0.5300
D)0.7019
E)0.7899

Question 70

Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers.Accordingly,he plans a sample of waiting times for walk-in customers.If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,the probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes is ___.

A)0.9974
B)0.4987
C)0.9772
D)0.4772
E)0.5000

Question 71

Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers.Accordingly,he plans a sample of waiting times for walk-in customers.If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,the probability that Albert's sample of 64 will have a mean less than 16 minutes is ___.

A)0.4772
B)0.0228
C)0.9072
D)0.9544
E)0.9772

Question 72

A carload of steel rods has arrived at Cybermatic Construction Company.The car contains 50,000 rods.Claude Ong,manager of Quality Assurance,directs his crew measure the lengths of 100 randomly selected rods.If the population of rods has a mean length of 120 centimetres and a standard deviation of 0.05 centimetres,the probability that Claude's sample has a mean between 119.985 and 120.0125 centimetres is ___.

A)0.9925
B)0.9974
C)0.9876
D)0.9544
E)0.9044

Question 73

A carload of steel rods has arrived at Cybermatic Construction Company.The car contains 50,000 rods.Claude Ong,manager of Quality Assurance,directs his crew measure the lengths of 100 randomly selected rods.If the population of rods has a mean length of 120 centimetres and a standard deviation of 0.05 centimetres,the probability that Claude's sample has a mean greater than 120.0125 centimetres is ___.

A)0.0124
B)0.0062
C)0.4938
D)0.9752
E)1.0000

Question 74

Suppose 40% of all seniors have a computer at home and a sample of 64 is taken.What is the probability that more than 30 of those in the sample have a computer at home?

A)0.3686
B)0.1314
C)0.8686
D)0.6314
E)0.1343

Question 75

Catherine Chao,Director of Marketing Research,needs a sample of Ottawa households to participate in the testing of a new toothpaste package.If 40% of the households in Ottawa prefer the new package,the probability that Catherine's random sample of 300 households will have a sample proportion between 0.35 and 0.45 is ___.

A)0.9232
B)0.0768
C)0.4616
D)0.0384
E)0.8976

Question 76

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system.If 10% of the 5,000 payroll vouchers issued since January 1,2000,have irregularities,the probability that Pinky's random sample of 200 vouchers will have a sample proportion of between .06 and .14 is ___.

A)0.4706
B)0.9706
C)0.0588
D)0.9412
E)0.8765