Deck 7: Sampling and Sampling Distributions

Question 1

The central limit theorem states that if the sample size,n,is large enough (n ≥20),the distribution of the sample means is normally distributed regardless of the shape of the population.

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

Sampling errors cannot by determined objectively for nonrandom sampling techniques.

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

The mean of the sample means is the same as the mean of the population

Question 15

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

Question 16

Systematic sampling is a type of random sampling technique.

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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 22

The sampling distribution of the sample means is close to the normal distribution only if the distribution of the population is close to normal.

Question 23

Paige DeMarco is the Vice President for University Advancement at State University. She is responsible for the capital campaign to raise money for the new student services building.Paige selects the first 100 alumni listed on a web-based social networking site for State University.She intends to contact these individuals regarding possible donations.Her sample is a _________.

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

Question 24

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 25

The sampling distribution of has a mean equal to the square root of the population
proportion p.

Question 26

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 27

Suppose 90% of students in some specific college have a computer at home and a sample of 40 students is taken. The probability that more than 30 of those in the sample have a computer at home can be approximated using the normal approximation.

Question 28

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 29

The sampling distribution of the sample means is less variable than the population distribution.

Question 30

Financial analyst Larry Potts needs a sample of 100 securities listed on either the New York Stock Exchange (NYSE)or the American Stock Exchange (AMEX). According to the Wall Street Journal's "Stock Market Data Bank," 2,531 NYSE securities and AMEX 746 securities were traded on the previous business day. Larry directs his staff to randomly select 77 NYSE and 23 AMEX 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 31

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 32

Financial analyst Larry Potts needs a sample of 100 securities listed on the New York Stock Exchange. In the current issue of the Wall Street Journal,2,531 securities are listed in the "New York 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 33

Financial analyst Larry Potts needs a sample of 100 securities listed on the New York Stock Exchange. In the current issue of the Wall Street Journal,2,531 securities are listed in the "New York 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 34

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 35

Paige DeMarco is the Vice President for University Advancement at State University. She is responsible for the capital campaign to raise money for the new student services building.Paige plans to target alumni and acquires her sampling frame from the State University Office of Alumni Relations.She intends to contact these individuals regarding possible donations. She randomly selects the sixth name as a starting point and then selects every 100th subsequent name (106,206,306,etc.). Her sample is a _________.

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

Question 36

The sampling distribution of is close to normal provided that n≥30.

Question 37

Paige DeMarco is the Vice President for University Advancement at State University. She is responsible for the capital campaign to raise money for the new student services building.Paige plans to target alumni and acquires her sampling frame from the State University Office of Alumni Relations.She intends to contact these individuals regarding possible donations.Paige chooses her sample by selecting six-digit numbers (1 to 150,000)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 38

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 39

If the population is normally distributed,the sample means of size n=5 are normally
distributed.

Question 40

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 41

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 42

Suppose a population has a mean of 870 and a variance of 8,100.If a random sample of 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 43

Decreasing 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 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

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean of less than $92 is _______.

A) 0.3400
B) 0.1600
C) 0.0000
D) 1.0000
E) 0.7000

Question 46

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 47

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's sample is a ________________.

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

Question 48

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 49

Suppose a population has a mean of 870 and a variance of 1,600.If a random sample of 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 50

Suppose a population has a mean of 450 and a variance of 900.If a random sample of 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 51

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 52

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 53

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 54

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a sample mean between $112 and $115 is _______.

A) 0.9738
B) 0.7777
C) 0.7823
D) 0.1915
E) 1.7561

Question 55

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 56

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean of more than $115 is _______.

A) 0.9738
B) 0.4738
C) 0.0262
D) 0.6103
E) 0.1103

Question 57

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a sample mean between $100 and $115 is _______.

A) 0.9738
B) 0.4738
C) 0.0262
D) 0.6103
E) 0.1103

Question 58

According to the central limit theorem,if a sample of size 56 is drawn from a population with a standard deviation of 14,the standard deviation of the distribution of the sample means would equal _______.

A) 14
B) 1.87
C) 3.5
D) 0.25
E) 3.74

Question 59

According to the central limit theorem,if a sample of size 56 is drawn from a population with a mean of 16,the mean of all sample means would equal _______.

A) 56
B) 16
C) 7.5
D) 44.0
E) 196

Question 60

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's sample is a ________________.

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

Question 61

Suppose 40% of all college students 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 62

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

Question 63

Suppose 40% of the population of pre-teens have a TV in their bedroom.If a random sample of 500 pre-teens is drawn from the population,then the probability that 44% or fewer of the pre-teens have a TV in their bedroom is _______.

A) 0.9644
B) 0.4644
C) 0.0356
D) 0.0400e) 0.9600

Question 64

Suppose 40% of the population of pre-teens have a TV in their bedroom.If a random sample of 500 pre-teens is drawn from the population,then the probability that between 36% and 44% of the pre-teens have a TV in their bedroom is _______.

A) 0.9644
B) 0.4644
C) 0.0356
D) 0.9328
E) 0.0712

Question 65

Suppose 30% of the U.S.population has green eyes.If a random sample of size 1200 U.S.citizens is drawn,then the probability that less than 348 U.S.citizens have green eyes is _______.

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

Question 66

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 67

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 68

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 69

Catherine Chao,Director of Marketing Research,needs a sample of Kansas City households to participate in the testing of a new toothpaste package. If 40% of the households in Kansas City 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 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 less than 15 minutes is ________.

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

Question 71

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 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 have a mean length of 120 inches and a standard deviation of 0.05 inch,the probability that Claude's sample has a mean less than 119.985 inches is _____________.

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

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 inches and a standard deviation of 0.05 inch,the probability that Claude's sample has a mean greater than 120.0125 inches is _____________.

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

Question 74

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 inches and a standard deviation of 0.05 inch,the probability that Claude's sample has a mean between 119.985 and 120.0125 inches is ____________.

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

Question 75

A random sample of size 100 is drawn from a population with a standard deviation of 10.If only 5% of the time a sample mean greater than 20 is obtained,the mean of the population is ______

A) 18.35
B) 16.25
C) 17.2
D) 20
E) 19

Question 76

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 77

Suppose 40% of the population of pre-teens have a TV in their bedroom.If a random sample of 500 pre-teens is drawn from the population,then the probability that 44% or more of the pre-teens have a TV in their bedroom is _______.

A) 0.9644
B) 0.4644
C) 0.0356
D) 0.0400
E) 0.9600

Question 78

Suppose 40% of all college students 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 79

Catherine Chao,Director of Marketing Research,needs a sample of Kansas City households to participate in the testing of a new toothpaste package. If 40% of the households in Kansas City 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 80

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