Deck 7: Sampling and Sampling Distributions

Question 1

The sampling method in which a population is divided into blocks and then selected by choosing a random mechanism is called a:

A) random sampling
B) systematic sampling
C) stratified sampling
D) cluster sampling

Answer 1

systematic sampling

Question 2

A sample chosen in such a way that every possible subset of same size has an equal chance of being selected is called a(n):

A) interval estimation
B) point estimation
C) simple random sample.
D) statistic

Answer 2

simple random sample.

Question 3

Selecting a random sample from each identifiable subgroup within a population is called:

A) demographic sampling
B) systematic sampling
C) stratified sampling
D) cluster sampling
E) none of these choices

Answer 3

stratified sampling

Question 4

Which of the following is not a consideration when determining appropriate sample size?

A) the cost of sampling
B) the timely collection of the data
C) interviewer fatigue
D) the likelihood of nonsampling error

Question 5

Potential sample members, called sampling units, are:

A) people
B) companies
C) households
D) all of these choices

Question 6

A list of all members of the population is called a:

A) sampling unit
B) probability sample
C) frame
D) relevant population

Question 7

Which statement is true of proportional sample sizes?

A) The proportion of a stratum in the sample is independent of the proportion of that stratum in the population.
B) The proportion of a stratum in the sample is the same as the proportion of that stratum in the population.
C) The proportion of a stratum in the sample is greater than the proportion of that stratum in the population.
D) The proportion of a stratum in the sample is less than the proportion of that stratum in the population.

Question 8

In systematic sampling, one of the first k members is selected randomly, and then every k^th member after this one is selected. The value k is called the sampling interval and equals the ratio N / n, where N is the population size and n is the desired sample size.

Question 9

In sampling, a population is:

A) the set of all humans
B) the set of all members about which a study intends to make inferences
C) any group of test subjects
D) a random group of individuals, households, cities, or countries

Question 10

A list of all members of the population from which we can choose a sample is called a frame, and the potential sample members are called sampling units.

Question 11

A probability sample is a sample in which the sampling units are chosen from the population by means of a random mechanism such as a random number table.

Question 12

We can measure the accuracy of judgmental samples by applying some simple rules of probability. This way, judgmental samples are not likely to contain our built-in biases.

Question 13

A sample in which the sampling units are chosen from the population by means of a random mechanism is a:

A) probability sample
B) judgmental sample
C) stratified sample
D) systematic sample

Question 14

Which of the following are reasons for why simple random sampling is used infrequently in real applications?

A) Samples can be spread over a large geographic region.
B) Simple random sampling requires that all sampling units be identified prior to sampling.
C) Simple random sampling can result in underrepresentation or overrepresentation of certain segments of the population.
D) All of these choices are valid reasons.

Question 15

A simple random sample is one where each member of the population has a known chance (this may differ from one member to another) or probability of being chosen.

Question 16

Identifiable subpopulations within a population are called:

A) clusters
B) samples
C) blocks
D) strata
E) none of these choices

Question 17

A judgmental sample is a sample in which the:

A) sampling units are chosen using a random number table
B) quality of sampling units judged before they are added to the sample
C) sampling units are chosen according to the sampler's judgment
D) sampling units are all biased and vocal about it

Question 18

Simple random samples are samples in which each member of the population has the same chance of being chosen.

Question 19

The defining property of a simple random sample is that:

A) every sample of a particular size has the same chance of being chosen
B) the easiest method to access samples are chosen
C) the fewest samples necessary for statistical significance are chosen
D) every fourth subject is chosen as a sample

Question 20

In stratified sampling, the population is divided into relatively homogeneous subsets called strata, and then random samples are taken from each stratum.

Question 21

Stratified samples are typically not used in real applications because they provide less accurate estimates of population parameters for a given sampling cost.

Question 22

The primary advantage of cluster sampling is sampling convenience (and possibly less cost). The downside, however, is that the inferences drawn from a cluster sample can be less accurate, for a given sample size, than for other sampling plans.

Question 23

A sales manager for a company that makes commercial ovens for restaurants is interested in estimating the average number of restaurants in all metropolitan areas across the entire country. He does not have access to the data for each metropolitan location, so he had decided to select a sample that will be representative of all such areas, and will use a sample size of 30. Do you believe that simple random sampling is the best approach to obtaining a representative subset of the metropolitan areas in the given frame? Explain. If not, recommend how the sales manager might proceed to select a better sample of size 30 from this data?

Question 24

The finite population correction factor is a correction for the standard error when the sample size is fairly large relative to the population size.

Question 25

A statistics professor has just given the final examination in his introductory statistics course. In particular, he is interested in learning how his class of 50 students performed on this exam. The data are shown below.
(A) Using these 50 students as the frame, use Excel to generate a simple random sample of size 10 from this frame.
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(B) Compute the mean scores in the frame and the simple random sample you generated in (A).
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(C) Compare the mean scores you computed in (B). Is your simple random sample a good representative of the frame? Why or why not?
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(D) Using these 50 students as the frame, use Excel to generate a systematic sample of size 10 from this frame.
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(E) Compare the mean scores in the frame with that in the systematic sample in (D). What do you conclude?

Question 26

The key to using stratified sampling is:

A) identifying the strata
B) selecting the appropriate strata
C) defining the strata
D) randomizing the strata

Question 27

Consider the frame of 50 full-time employees of Computer Technologies, Inc (CTI). CTI's human resources manager has collected annual salary figures for all employees and she has calculated a mean of $47,723, a median of $41,082 and a standard deviation of $24,167. A simple random sample of 10 employees is presented below (salary is in $1,000's). Compute the mean, median, and standard deviation for the sample and compare these statistics with the measures for the entire company.

Question 28

In cluster sampling, the population is divided into subsets called clusters (such as cities or city blocks), and then a random sample of the clusters is selected. Once the clusters are selected, we typically sample all of the members in each selected cluster.

Question 29

Systematic sampling is generally similar to simple random sampling in its statistical properties.

Question 30

In stratified sampling with proportional sample sizes, the proportion of each stratum selected differs from stratum to stratum.

Question 31

A statistics professor has just given the final examination in his introductory statistics course. In particular, he is interested in learning how his class of 50 students performed on this exam. The data are shown below.
(A) Technically, this process does not yield a random sample of the books in the store. Why not?
(B) How could a truly random sample be obtained?

Question 32

One obvious advantage of stratified sampling is that we obtain separate estimates within each stratum - which we would not obtain if we took a simple random sample from the entire population. A more important advantage is that we can increase the accuracy of the resulting population estimates by using appropriately defined strata.

Question 33

Cluster sampling is often less convenient and more costly than other random sampling methods.

Question 34

Which of the following statements correctly describe estimation?

A) It is the process of inferring the values of known population parameters from those of unknown sample statistics.
B) It is the process of inferring the values of unknown sample statistics from those of known population parameters.
C) It is the process of inferring the values of known sample statistics from those of unknown population parameters.
D) It is the process of inferring the values of unknown population parameters from those of known sample statistics.

Question 35

The probability of being chosen in a simple random sample of size n from a population of size N is:

A) 1/N
B) N - 1/n
C) N/n
D) n/N

Question 36

Sally Bird of Big Rapids Realty has received data on 60 houses that were recently sold in Mecosta County in Michigan. The data are recorded in the table shown below. Included in this data set are observations for each of the following variables:
· The appraised value of each house (in thousands of dollars)
· The selling price of each house (in thousands of dollars)
· The size of each house (in hundreds of square feet)
· The number of bedrooms in each house
(A) Suppose that Sally wishes to examine a representative subset of these 60 houses that has been stratified by the number of bedrooms. Use Excel to assist her by finding such a stratified sample of size 10 with proportional sample sizes.
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(B) Explain how Sally could apply cluster sampling in selecting a sample of size 15 from this frame.
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(C) What are the advantages and disadvantages of employing cluster sampling in this case?

Question 37

The standard error of sample mean is large when the observations in the population are spread out (large ), but that the standard error can be reduced by taking a smaller sample.

Question 38

Simple random sampling can result in under-representation or over-representation of certain segments of the population. This is one of several reasons that simple random samples are almost never used in real applications.

Question 39

A sampling error is the result of:

A) measurement error
B) nonresponse bias
C) nontruthful responses
D) "unlucky" sampling

Question 40

If systematic sampling is chosen as the sampling technique, it is probably because:

A) systematic sampling has better statistical properties than simple random sampling
B) systematic sampling is more convenient
C) systematic sampling always results in more representative sampling than simple random sampling
D) none of these choices

Question 41

The approximate standard error of the sample mean is calculated as:

A)
B)
C)
D)

Question 42

There is an approximately _____% chance that any particular will be within two standard deviations of the population mean ( ).

A) 90
B) 95
C) 99
D) 99.7

Question 43

The standard deviation of is usually called the:

A) standard error of the mean
B) standard error of the sample
C) standard error of the population
D) randomized standard error

Question 44

When we sample less than 5% of the population, the finite population correction factor; fpc = , is used to modify the formula for the standard error of the sample mean.

Question 45

The approximate 95% confidence interval for a population mean is:

A)
B)
C)
D)

Question 46

Non-truthful response is a particular problem when:

A) sensitive questions are asked
B) surveys are anonymous
C) interviewers are not trained
D) the sample is from an unusual population

Question 47

The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:

A) central limit theorem
B) central tendency theorem
C) simple random sample theorem
D) point estimate theorem

Question 48

When a portion of the sample does not respond to the survey, ____ has occurred.

A) a measurement error
B) nonresponse bias
C) a sampling error
D) systematic failure
E) a nonlinear error

Question 49

The two basic sources for error when using random sampling are:

A) sampling and selection
B) identification and selection
C) sampling and nonsampling
D) bias and randomness
E) linear and nonlinear

Question 50

Which of the following statements are correct?

A) A point estimate is an estimate of the range of a population parameter
B) A point estimate is a single value estimate of the value of a population parameter
C) A point estimate is an unbiased estimator if its standard deviation is the same as the actual value of the population standard deviation
D) All of these choices are correct

Question 51

Measurement error occurs when:

A) a portion of the sample does not respond to the survey
B) the sample responses are not clear
C) the responses to question do not reflect what the investigator had in mind
D) the investigator does not correctly tally all responses

Question 52

The averaging effect means that as you average more and more observations from a given distribution, the variance of the average:

A) increases
B) decreases
C) is unaffected
D) could either increase, decrease, or stay the same

Question 53

The central limit theorem (CLT) is generally valid for:

A) n > 5
B) n > 10
C) n > 20
D) n > 30
E) any size n

Question 54

The opportunity for sampling error is decreased by:

A) larger sample sizes
B) smaller sample sizes
C) affluent samples
D) educated samples

Question 55

The accuracy of the point estimate is measured by its:

A) standard deviation
B) standard error
C) sampling error
D) nonsampling error

Question 56

The finite population correction factor, , should generally be used when:

A) N is any finite size
B) n is less than 5% of the population size N
C) n is greater than 5% of the population size N
D) n is any finite size

Question 57

The sampling mean is the ____ estimate for the population mean .

A) random
B) point
C) simple
D) interval

Question 58

Which of the following statements is correct?

A) A confidence interval describes a range of values that is likely not to include the actual population parameter
B) A confidence interval is an estimate of the range for a sample statistic.
C) A confidence interval is an estimate of the range of possible values for a population parameter.
D) None of these statements is correct.

Question 59

Sampling error is evident when:

A) a question is poorly worded and results in bias
B) the sample is too small
C) the sample is not random
D) the sample mean differs from the population mean

Question 60

An unbiased estimator is a sample statistic:

A) used to approximate a population parameter
B) which has an expected value equal to the value of the population parameter
C) whose value is usually less than the population parameter
D) that incorporates the standard error of the mean

Question 61

The standard error of the estimate measures how much estimates vary from sample to sample.

Question 62

An estimator is said to be unbiased if the mean of its sampling distribution equals the value of the population parameter being estimated.

Question 63

Voluntary response bias occurs when the responses to questions do not reflect what the investigator had in mind.

Question 64

The opportunity for nonsampling error is increased by:

A) larger sample sizes
B) smaller sample sizes
C) affluent samples
D) educated samples

Question 65

The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.

Question 66

An unbiased estimate is a point estimate such that the mean of its sampling distribution is equal to the true value of the population parameter being estimated.

Question 67

The difference between the point estimate and the true value of the population parameter being estimated is called the estimation error.

Question 68

The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

Question 69

The central limit theorem (CLT) states that the sampling distribution of the mean is approximately normal, no matter what the distribution of the population, as long as the sample size is large enough.

Question 70

The mean of the sampling distribution of always equals:

A) the population mean
B) / n
C) the population standard deviation
D) / n

Question 71

The standard error of an estimate is the standard deviation of the sampling distribution of the estimate. It measures how much estimates from different samples vary.

Question 72

When the sample size is greater than 5% of the population, the formula for the standard error of the mean should be modified with a finite population correction.

Question 73

A confidence interval is an interval calculated from the population data, where we strongly believe the true value of the population parameter lies.

Question 74

It is customary to approximate the standard error of the sample mean by substituting the sample standard deviation s for in the formula: SE( ) = .

Question 75

Estimation is the process of inferring the value of an unknown population parameter using data from a random sample

Question 76

A point estimate is a single numeric value, a "best guess" of a population parameter, calculated from the sample data.

Question 77

A sample of size 20 is selected at random from a population of size N. If the finite population correction factor is 0.9418, then N must be 169.

Question 78

The randomized response technique is a way of getting at sensitive information to avoid estimation errors due to nontruthful responses.

Question 79

The sampling distribution of any point estimate (such as the sample mean or proportion) is the distribution of the point estimates we would obtain from all possible samples of a given size drawn from the population.

Question 80

The central limit theorem (CLT) is considered to be an important result in statistics because:

A) the CLT allows us to assume that the population distribution is approximately normal, provided n is reasonably large
B) the CLT allows us to estimate the population mean without knowing the exact form of the population distribution, provided n is reasonably large
C) the CLT allows us to construct confidence intervals for the population mean without knowing the exact form of the population distribution, provided n is reasonably large
D) of all of these choices