Deck 8: Sampling Methods and the Central Limit Theorem

Question 1

It is often not feasible to study the entire population because it is impossible to observe all the items in the population.

Answer 1

True

Question 2

The items or individuals of the population are arranged in a file drawer alphabetically by date received.A random starting point is selected and then every k^th member of the population is selected for the sample.This sampling method is called simple random sampling.

Answer 2

False

Question 3

Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive.

Answer 3

True

Question 4

If the size of a sample equals the size of the population,we would not expect any error in estimating the population parameter.

Question 5

A simple random sample assumes that each item or person in the population has an equal chance of being included.

Question 6

When systematic random sampling is used,the central limit theorem cannot be applied.

Question 7

The central limit theorem implies that for adequate sample size,the sampling distribution of the sample mean is approximately normal.

Question 8

In stratified random sampling,a population is divided into strata using naturally occurring geographic or other boundaries.Then strata are randomly selected and a random sample is collected from each strata.

Question 9

The standard error of the mean is also called sampling error.

Question 10

In stratified random sampling,a population is divided into subgroups called strata and a sample is randomly selected from each stratum.

Question 11

If a population is not normally distributed,the sampling distribution of the sample means tends to approximate a normal distribution.

Question 12

A sampling distribution of the means is a probability distribution consisting of a list of all possible sample means of a given sample size selected from a population and the probability of occurrence associated with each sample mean.

Question 13

The central limit theorem implies that for samples of size one or two,we can infer that the sampling distribution of the sample mean is approximately normal.

Question 14

When using systematic random sampling,the sampling error will be zero.

Question 15

For a simple random sample,each item in the population has an equal chance of being chosen.

Question 16

We can expect some difference between sample statistics and the corresponding population parameters.This difference is called the sampling error.

Question 17

When cluster sampling is used,the central limit theorem cannot be applied.

Question 18

In cluster sampling,a population is divided into subgroups called clusters and a sample is randomly selected from each cluster.

Question 19

When using stratified random sampling,the sampling error will be zero.

Question 20

In cluster sampling,a population is divided into clusters using naturally occurring geographic or other boundaries.Then clusters are randomly selected and a random sample is collected from each cluster.

Question 21

When all the items in a population have an equal chance of being selected for a sample,the process is called __________________.

A)Random sampling
B)z-score
C)Sampling error
D)Nonprobability sampling

Question 22

The standard error of the mean will vary according to the size of the sample.As the sample size n gets larger,the variability of the sample means gets smaller.

Question 23

When dividing a population into subgroups so that a random sample from each subgroup can be collected,what type of sampling is used?

A)Simple random sampling
B)Systematic sampling
C)Stratified random sampling
D)Cluster sampling

Question 24

Fish and game wardens estimate the average weight of the fish or game population by using creel checks and other devices.Based on this sample data,a warden might estimate that the mean weight of Coho salmon caught in Lake Michigan is 2.5 pounds.This single number is called a point estimate of the unknown population parameter.

Question 25

If the sample size keeps getting larger and larger and finally equals the size of the population,there would be no error in predicting the population mean because the sample size and the size of the population would be the same.

Question 26

If 40 samples of size 21 were selected from a population of 22,493,we would expect the mean of the sample means and the population mean to be close but not exactly equal.

Question 27

Based on the central limit theorem,sampling error will decrease as sample size increases.

Question 28

Based on the sampling distribution of the means and the central limit theorem,the sample mean can be used as a good estimator of the population mean,assuming that the size of the sample is sufficiently large.

Question 29

Suppose we select every fifth invoice in a file.What type of sampling is this?

A)Random
B)Cluster
C)Stratified
D)Systematic

Question 30

All possible samples of size n are selected from a population and the mean of each sample is determined.What is the mean of the sample means?

A)Exactly the same as the population mean
B)Larger than the population mean
C)Smaller than the population mean
D)Cannot be estimated in advance

Question 31

The mean of all possible sample means is equal to the population mean.

Question 32

The Central Limit Theorem states that for a sufficiently large sample the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to µ and the variance equal to $\sigma$ ²/n.

Question 33

An estimate of the population mean based on a large sample is less reliable than an estimate made using a small sample.

Question 34

The Central Limit Theorem states that for a sufficiently large sample the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to $\sigma$ ²and the variance equal to $\sigma$ ^2/n.

Question 35

To determine the value of the standard error of the mean,the total error is divided by the sample size.

Question 36

The Central Limit Theorem states that if the sample size,n,is sufficiently large,the sampling distribution of the means will be approximately normal no matter whether the population is normally distributed,skewed,or uniform.

Question 37

What sample statistic is used to estimate a population parameter?

A)Parameter
B)Sampling error
C)Point estimate
D)Interval estimate

Question 38

Based on the central limit theorem,sampling error will decrease as sample size decreases.

Question 39

The true sampling error is usually not known because

A)µ is a unknown
B)µ is a random variable
C) $\sigma$ ² is unknown
D)The sample mean cannot be computed

Question 40

What is the difference between a sample mean and the population mean called?

A)Standard error of the mean
B)Sampling error
C)Interval estimate
D)Point estimate

Question 41

Sampling error is defined as

A)( - µ)
B) $\sigma$
C) $\sigma$ /n
D)N - n

Question 42

Sampling error is the difference between a corresponding sample statistic and the

A)sample mean.
B)biased sample.
C)population parameter.
D)chance error.

Question 43

The mean of all possible sample means is equal to the

A)population variance.
B) .
C)sample variance.
D)population mean.

Question 44

A statewide sample survey is to be made.First,the state is subdivided into counties.Seven counties are selected at random and further sampling is concentrated on these seven counties.What type of sampling is this?

A)Simple random
B)Systematic random sampling
C)Cluster
D)Stratified

Question 45

Suppose a research firm conducted a survey to determine the average amount of money steady smokers spend on cigarettes during a week.A sample of 100 steady smokers revealed that the sample mean is $20 and the sample standard deviation is $5.What is the probability that a sample of 100 steady smokers spend between $19 and $21?

A)0.4772
B)0.0228
C)0.9544
D)$20

Question 46

Based on the central limit theorem,the size of the sampling error is

A)Directly related to the sample size,i.e. ,the larger the sample size the larger the sampling error.
B)Directly related to the population mean,i.e. ,the larger the mean,the larger the sampling error.
C)Inversely related to the sample size,i.e. ,the larger the sample size the smaller the sampling error.
D)Inversely related to the population standard deviation,i.e. ,the smaller the standard deviation,the larger the sampling error.

Question 47

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the average time to complete a tax form?

A)The population distribution is skewed to the right.
B)The population distribution is skewed to the left.
C)The population distribution is normal.
D)The shape of the population distribution does not matter.

Question 48

Which of the following is the standard error of the mean?

A) $\sigma$
B)x/n
C)
D)s

Question 49

The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond.A sample of the weights of 40 trout revealed that the mean weight is 402.7 grams and the standard deviation 8.8 grams.What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

A)0.3783
B)0.0228
C)1.0
D)0.5

Question 50

As the size of the sample increases,what happens to the shape of the distribution of sample means?

A)Cannot be predicted in advance
B)Approaches a normal distribution
C)Positively skewed
D)Negatively skewed

Question 51

A marketing firm is studying consumer preferences for winter fashions in four different months.From a population of women,18-21 years of age,a random sample of 100 women was selected in January.Another random sample of 100 women was selected in March.Another random sample of 100 women was selected in June.Another random sample of 100 women was selected in September.

A)The sample size was 4.
B)The sample size was 100.
C)The sample size was 400.
D)The sample size was 1.

Question 52

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires.The average tread wear was found to be 50,000 miles with a standard deviation of 3,500 miles.What is the best estimate of the average tread life in miles for the entire population of these tires?

A)50,000
B)3,500
C)(50,000/100)
D)(3,500/100)

Question 53

Based on the central limit theorem,for a given population,the mean of all the sample means ( )of sample size n,and the mean of all (N)population observations (x)are

A)equal to
B)not equal
C)are equal to ( - x)
D)equal to the population mean,µ

Question 54

An experiment involves selecting a random sample of 256 middle managers at random for study.One item of interest is their mean annual income.The sample mean is computed to be $35,420 and the sample standard deviation is $2,050.What is the standard error of the mean?

A)$128.125
B)$138.36
C)$2,050
D)$8.01

Question 55

For a population that is not normally distributed,the distribution of the sample means will

A)be negatively skewed.
B)approach the normal distribution.
C)be positively skewed.
D)take the same shape as the population.

Question 56

For a distribution of sample means constructed by sampling 5 items from a population of 15,

A)the sample size is 15
B)there will be 3003 possible sample means
C)the mean of the sample means will be 3
D)the standard error will be 1

Question 57

Manufacturers were subdivided into groups by volume of sales.Those with more than $100 million in sales were classified as Class A large;those from $50 to $100 million as Class A medium size;and those between $25 and $50 million... ,and so on.Samples were then selected from each of these groups.What is this type of sampling called?

A)Simple random
B)Stratified random
C)Cluster
D)Systematic

Question 58

Based on the central limit theorem,the mean of all the sample means is

A)
B)µ
C) $\sigma$
D) $\alpha$

Question 59

The mean weight of trucks traveling on a particular section of I-475 is not known.A state highway inspector needs an estimate of the mean.He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons,with a standard deviation of the sample of 4.2 tons.What is probability that a truck will weigh less than 14.3 tons?

A)0.0062
B)0.3632
C)0.1368
D)0.4938

Question 60

A marketing firm is studying consumer preferences for winter fashions in four different months.From a population of women,18-21 years of age,a random sample of 100 women was selected in January.Another random sample of 100 women was selected in March.Another random sample of 100 women was selected in June.Another random sample of 100 women was selected in September.

A)The number of samples was 4.
B)The number of samples was 100.
C)The number of samples was 400.
D)The number of samples was 1.

Question 61

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spend studying per week.Based on a simple random sample,they surveyed 144 students.The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours.What is the probability that a sample mean would exceed 20 hours per week?

A)1.0
B)0.5
C)1.96
D)Cannot be calculated based on the given information.

Question 62

Sometimes,sampling from a population may be preferred because collecting statistics may require that products be ___________.

Question 63

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spend studying per week.Based on a simple random sample,they surveyed 144 students.The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours.What is the standard error of the mean?

A)0.83
B)10
C)0.5
D)2

Question 64

The Intelligence Quotient (IQ)test scores are normally distributed with a mean of 100 and a standard deviation of 15.What is the probability that a person would score between 85 and 115?

A)0.3413
B)0.6826
C)1.00
D)Very likely

Question 65

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What is the probability that the mean completion time is between 1 and 2 hours,i.e. ,60 and 120 minutes?

A)Approximately 1
B)0.1664
C)0.8336
D)0.9676

Question 66

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.You bought four tires.What is the probability that the average mileage of the four tires exceeds 66,000 miles?

A)0.0013
B)0.9987
C)0.4987
D)0.9544

Question 67

The Intelligence Quotient (IQ)test scores are normally distributed with a mean of 100 and a standard deviation of 15.Given a class with 25 students,what is the probability that the class' average IQ score is between 85 and 115?

A)0.4987
B)3.00
C)0.0026
D)0.9974

Question 68

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.What is the probability that a tire lasts between 54,000 and 66,000 miles?

A)0.4332
B)0.8664
C)1.00
D)Very likely

Question 69

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spend studying per week.Based on a simple random sample,they surveyed 144 students.The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours.What is the probability of finding a sample mean less than 18 hours?

A)0.4820
B)0.4920
C)0.0080
D)0.0180

Question 70

The Intelligence Quotient (IQ)test scores are normally distributed with a mean of 100 and a standard deviation of 15.You enrolled in a class of 25 students.What is the probability that the class' average IQ exceeds 130?

A)0.0228
B)0.9772
C)Approximately zero
D)0.9544

Question 71

Sampling from a population may be preferred because studying all the items in a population may be too _____________.

Question 72

What type of sampling is it when a population is first divided into subgroups and then a sample is selected from each subgroup? _________

Question 73

Auditors may select every 20^thfile starting with say,the 5^thfile in the top drawer.Then file numbers 25,45,65,85,...are audited.What type of sampling is this? _________________

Question 74

The Intelligence Quotient (IQ)test scores are normally distributed with a mean of 100 and a standard deviation of 15.What is the probability that a person would score 130 or more on the test?

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

Question 75

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What is the standard error of the mean?

A)14 minutes
B)140 minutes
C)1.4 minutes
D)90 minutes

Question 76

Sampling from a population may be preferred because,contacting or listing the entire population would be too ___________ consuming.

Question 77

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.For a set of four tires,what is the probability that the average tire life is between 57,000 and 63,000 miles?

A)0.4332
B)0.8664
C)1.00
D)Very likely

Question 78

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What is the probability that the mean completion time will be more than 120 minutes?

A)Approximately zero
B)0.0832
C)0.4168
D)0.0162

Question 79

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spend studying per week.Based on a simple random sample,they surveyed 144 students.The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours.What is the probability that average student study time is between 18 and 22 hours?

A)0.9640
B)0.0160
C)0.0360
D)0.9840

Question 80

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.What is the probability that a tire will last 72,000 miles or more?

A)0.0013
B)0.9987
C)0.4987
D)0.9544