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Chapter 7: Sampling

TRUE/FALSE

1) Researching with a full census of the population is always more accurate than using only a

sample of that population.

Answer: False

Although there is no sampling error in a census, non-sampling error can be higher than

combined sampling and non-sampling errors for a sample.

2) The most common elements in marketing research sampling are business entities.

Answer: False

The most common elements are individual persons.

3) Judgment sampling is superior to convenience sampling because the sampling error of the

former can be ascertained.

Answer: False

Judgment sampling is a non-probability sampling method; sampling error cannot be

ascertained.

4) Quota samples are useful in preliminary stages of research. If done with great care, they

can provide clear, accurate, and useful information, even if they are likely to be less valid

than a probability sample.

Answer: True

Quota samples can be useful, especially for exploratory research.

5) If a quota sample matches the population along known characteristics, then it has been

demonstrated to be a valid sample.

Answer: False

A match between a sample and the population along known characteristics does not mean

anything about other characteristics. The error in other sample measures is of unknown size

and direction.

6) In probability sampling, the chance that a population element will be included in a sample

is equal to that of all other elements.

Answer: False

The probability is known, but it is not necessarily equal for all elements within a population.

7) Although simple random sampling is the simplest of the probability-based sampling

procedures, it is not used in marketing research projects as much as other sampling methods,

because of a higher probability of non-sampling error.

Answer: False

The simple random sample is utilized in the majority of marketing research projects

involving sampling, far more than any non-probability sampling procedure.

8) In sampling terminology, a parameter is any measurement taken of a sample.

Answer: False

In sampling terminology, a parameter is the true value of some quantity of interest in a

specific population. It is what is being estimated by sample values.

9) In practice, the purpose of a sample parameter is to estimate a population statistic.

Answer: False

It is the reverse, the purpose of a sample statistic is to estimate a population parameter.

10) For almost all variables, Greek letters are used for sample statistics and Roman (e.g.

English) letters are used for population parameters.

Answer: False

It is the reverse; Greek letters are used for population parameters and Roman letters for

sample statistics.

11) Statistical theory, specifically the central limit theorem, tells us that we can be 68 percent

certain that the true population mean lies within one standard error from the sample mean.

Answer: True

68 percent of the normal distribution curve lies within one standard error of the mean.

12) As the sample size increases, the confidence interval around a mean will also become

larger.

Answer: False

Because the square root of the sample size is in the denominator of the formula to calculate

the standard error, the confidence interval around a mean will become smaller as the sample

size increases.

13) The size of the sample is dramatically more important than the size of the population in

almost all statistical calculations in research.

Answer: True

Because populations used in most research are very large, the sample size becomes much

more critical.

14) If a researcher takes a census of a population, then the finite population correction factor

would be equal to 1, because the sample would include all of the population.

Answer: False

The finite population correction factor for a census is zero, because there is no standard error;

n = N.

15) Precision expressed in units is called relative precision.

Answer: False

Precision expressed in units is called absolute precision. Relative precision is expressed as a

percentage.

16) A small value for the coefficient of variation would indicate a relatively homogenous

population and that most data points are close to the mean.

Answer: True

The smaller the coefficient of variation, the tighter the distribution.

17) In the calculation of confidence levels, non-sampling errors are not accounted for at all.

Answer: True

Confidence levels only account for sampling error, not non-sampling errors.

18) Although sampling errors tend to decrease with sample size, non-sampling errors tend to

increase with sample size.

Answer: True

non-sampling errors normally increase with sample size, especially non-sampling errors that

create a bias in all of the data.

19) The size of a sample does not necessarily indicate a better study and more accurate

results.

Answer: True

The key is how the sample is selected and whether it is representative of the population.

20) Although stratified sampling can be less costly and easier to conduct, it will almost

always have a higher standard error of the estimator than a simple random sample.

Answer: False

If done correctly, the stratified sample will decrease the standard error of the estimator by

making sure the designated strata are more homogeneous.

21) One advantage of using stratified sampling is that researchers can obtain the same

precision as with an unstratified sample, but with a smaller sample and thus at a lower cost.

Answer: True

Stratified sampling allows for greater precision with the same sample size or the same level

of precision with a smaller sample.

22) If the groups developed in cluster sampling are exactly as heterogeneous as the

population, then the standard error of the cluster sample will be less than that of simple

random sampling.

Answer: False

If the cluster group is as heterogeneous as the population, the standard error will be the same

as with simple random sampling.

23) Systematic sampling is often used in practice because selecting a systematic sample is

easy and inexpensive.

Answer: True

In contrast to simple random sampling, systematic sampling does not require hopping all over

the sampling frame to gather elements.

24) One of the disadvantages of the area sampling is that it is limited to one or two stages.

Answer: False

Area sampling can have as many stages as needed or desired by the researcher.

25) Multistage area sampling is much less statistically efficient than simple random sampling.

Answer: True

In a simple random sample, a single sampling error is calculated. In multistage area sampling,

a sampling error is calculated for each stage of sampling.

MULTIPLE CHOICE

1) All of the following are major benefits sampling offers over taking a census except

a. a sample saves money

b. a sample saves time

c. a sample may be more inclusive

d. a sample may be more accurate

Answer: C

A census includes every member of the population; a sample does not.

2) A(n) _______________ is the unit about which we seek information, and it provides the

basis of the analysis that marketing researchers undertake.

a. element

b. population

c. sampling unit

d. sampling frame

Answer: A

The element is unit from which researchers seek information.

3) In single-stage sampling

a. different levels of sampling are utilized

b. only one characteristic of the sample is measured

c. the sampling units and elements are the same

d. the sample is larger than the population

Answer: C

With single stage sampling, the element is the same as the sampling unit.

4) A three-stage sampling process would require

a. one sampling frame

b. three sampling frames

c. six sampling frames

d. one sampling frame and a tertiary randomizing device

Answer: B

Every stage of a sampling process requires its own sampling frame.

5) A _______________ is, loosely speaking, what researchers wish to make inferences about

but for which researchers lack the resources (time, funds, energy) to conduct a full census.

a. sampling units

b. study population

c. sampling frame

d. sample element

Answer: B

For all practical purposes, the study population should be conceptualized as the aggregation

of elements from which the sample is actually selected, knowing it is virtually impossible to

select elements from an entire population.

6) The first step of sampling is to define the population. The second step is to

a. physically select the sample

b. mock up likely and extreme data values

c. decide on a sample size

d. identify the sampling frame

Answer: D

After the population is defined, the next step is to identify the sampling frame.

7) With probability sampling, each element of the population

a. has a known chance of being selected that is not necessarily equal

b. has an equal chance of being selected that is not necessarily known

c. has a known and equal chance of being selected

d. has an unknown chance of being selected because the sample is designed through quotas

Answer: A

With probability sampling, each element has a known chance of being selected, not

necessarily an equal chance of selection.

8) With non-probability sampling, each element of the population

a. has a known chance of being selected that is not necessarily equal

b. has an equal chance of being selected that is not necessarily known

c. has a known and equal chance of being selected

d. has an unknown chance of being selected

Answer: D

In non-probability sampling, the sample is designed through judgment, quotas or

convenience. The precise chance of selection is not known, and sampling error cannot be

calculated.

9) With simple random sampling, each element of the population

a. has a known chance of being selected that is not necessarily equal

b. has an equal chance of being selected that is not necessarily known

c. has a known and equal chance of being selected

d. has an unknown chance of being selected because the sample is designed through quotas

Answer: C

Simple random sampling is a special case of probability sampling in which each element has

an equal chance of being selected.

10) All of the following statements about convenience samples are true except

a. Sampling error cannot be calculated.

b. The sampling unit or element is self-selected.

c. It is not appropriate for exploratory research.

d. Conclusive statements about the results from a convenience sample cannot be made.

Answer: C

Convenience samples are not appropriate for conclusive research, but are for exploratory

research.

11) _______________ sampling involves explicit steps to model a population on some

prespecified “control” characteristic, typically demographic.

a. Stratified sampling

b. Judgment sampling

c. Quota sampling

d. Simple random sampling

Answer: C

With quota sampling, researchers strive to develop a sample based on a population’s

characteristics.

12) Which of the following is a example of judgment sampling?

a. For a major launch campaign for a brand of bath soap, three cities in California were

selected because there were deemed to be representative of the nation as a whole.

b. In a study of taste preferences for brands of soft drinks, a marketing research firm selected

a sample of 200 people from a large Chicago shopping mall over one weekend.

c. All of the department stores within 50 miles of the corporate office were selected for

testing a new point-of-purchase display.

d. From a list of all freshmen at a university, the school selected every 12th name to be

interviewed about their first year experience at the school.

Answer: A

Answer A is an example of judgment sampling since the towns selected were based on the

researcher’s judgment of being representative of the population. B and C are convenience

samples; D is a systematic sample.

13) If a quota sample has 3 control characteristics, each of which has 2 categories, the total

number of sampling cells required would be

a. 3

b. 5

c. 6

d. 8

Answer: D

2×2×2=8

14) Some quantity of interest in a specific population is a

a. parameter

b. statistic

c. variance

d. range

Answer: A

By definition, a parameter is some quantity of interest in a specific population.

15) Any quantity derived from a sample is a

a. parameter

b. statistic

c. variance

d. range

Answer: B

By definition, a statistic is any quantity derived from a sample.

16) The population mean of a continuous variable is denoted by which of the following

symbols?

a. x̄

b. s

c. s2

d. μ

e. σ

Answer: D

The population mean is denoted by m.

17) The measure of dispersion of the data around a sample mean is called

a. variance

b. the coefficient of dispersion

c. its degrees of freedom

d. the t statistic

Answer: A

By definition, variance is the measure of dispersion of the data around the mean.

18) Degrees of freedom is the

a. sample size – 1

b. sample size – number of statistics calculated from the same data

c. sample size – number of control characteristics used for the same data

d. sample size – number of variables within the same data

Answer: B

Degrees of freedom is the sample size (n) minus the number of statistics that will be

calculated.

19) The square root of the sample variance is

a. sigma (σ)

b. the standard deviation

c. the degrees of freedom

d. the half-width of the confidence interval

Answer: B

By definition, the standard deviation (s) is the square root of the sample variance (s2). Sigma

(σ) is square root of the population variance.

20) The variance of the sample consisting of the values 2, 4, 6, 8, 10 is

a. 6

b. 8

c. 10

d. 12

Answer: C

The variance is the sum of squared deviations divided by the degrees of freedom. S2 = SS/df

This can be calculated with the deviations from the mean (of 6) and the df = n – 1:

[(2 – 6)2 + (4 – 6)2 + (6 – 6)2 + (10 – 6)2] / (5 – 1) = (16 + 4 + 0 + 16)/4 = 10

Or one could use the computational formula of

= [(4 + 16 + 36 + 64 + 100) – (30)2/n] / (n – 1) = (220 – 180)/4 = 40/4 = 10

21) All statistical tests, such as calculation of the mean and standard error of the sampling

distribution can be calculated and are valid under the following condition(s):

a. the population is normal and the sample is any size

b. the population has an unknown distribution and the sample size is at least 30

c. both a and b

d. either a or b

Answer: D

For statistical tests to be valid, either the sample size has to be greater or equal to 30 or the

population has to be normally distributed.

22) If the standard deviation of a statistic X is 4.3 and the sample size is 16, what is the

standard error of the sampling distribution for X?

a. 0.269

b. 1.075

c. 8.295

d. 17.2

Answer: B

The standard error of the sampling distribution for X (

) is the standard deviation of X

divided by the square root of the sample size, in this case 4.3 / 4 = 1.075.

23) With a confidence interval of the sample mean equal to two standard errors, researchers

can be _______________ percent certain that the interval contains the true population mean.

a. 50

b. 68

c. 95

d. 99.7

Answer: C

For two standard errors, the confidence level is 95 percent.

24) If a researcher wants to improve the precision of a statistic by one decimal point, the

sample size would have to increase by _______________ times.

a. five

b. ten

c. 100

d. 1,000

Answer: C

Sample size increases with the square of the precision.

25) To check if the central limit theorem holds for a sample proportion (and therefore can be

used for calculating confidence intervals), the value calculated from np(1–p) should be

a. less than 1

b. greater than 5

c. less than 25

d. greater than 30

Answer: B

The value should be greater than 5. (Note that this is a guideline that statisticians have found

to work well in practice, not a natural law, and is often even stronger than one needed.)

26) For finite populations, the formula used for calculating the standard error of the sampling

distribution of the mean must be modified by the _______________.

a. inverse square law

b. standard deviation

c. finite correction factor

d. sample mean ± the confidence interval

Answer: C

With finite populations, the standard error of the sampling distribution is modified based on

the size of the population.

27) The coefficient of variation is the ratio of the

a. standard error of the sampling distribution to the mean

b. standard deviation to the mean

c. variance to the mean

d. standard deviation to the variance

Answer: B

By definition, the coefficient of variation is the ratio of the standard deviation to the mean.

28) To calculate the “optimal” sample size, all of the following information is needed except

a. precision required

b. level of confidence (a)

c. estimate of population variance

d. sample mean

Answer: D

The sample mean is not necessary to calculate the optimal sample size.

29) All of the following statements are true of the required sample size, except that

a. it varies inversely with the precision desired

b. it varies directly with the estimate of the population standard deviation

c. if varies inversely with the size of the population

d. it varies directly with the desired confidence level

Answer: C

The size of the population is not normally a factor in calculating the required sample size,

because most populations are relatively large.

30) Suppose a researcher is conducting a bivariate analysis with 5 categories for each variable

in the cross-tabulation. Using the practical rule of thumb, what is the recommended minimum

total sample size?

a. 30

b. 125

c. 150

d. 500

Answer: C

The cross-tabulation will include (5 × 2 = ) 10 cells, and the rule of thumb is a minimum of

15 cases per cell. Minimum sample size N = 10 × 15 = 150.

31) If done correctly, stratified sampling can actually decrease the standard error of the

estimator by

a. making sure the strata are more homogeneous on the variables for which statistics will be

calculated

b. making sure each strata forms a representative sample of the population

c. decreasing the number of categories within each of the variables for which statistics will be

calculated

d. making sure the sample is sufficiently large to ensure a lower sampling error

Answer: A

If the strata are more homogeneous than a simple random sample, the standard error of the

estimator will be less.

32) The first step in setting up a stratified sampling plan is to

a. select an independent random sample from each strata

b. analyze the strata for representativeness based on an external criterion variable

c. select every kth element in the sampling frame

d. divide the population into mutually exclusive and collectively exhaustive groups

Answer: D

Step 1 is to divide the sample into mutually exclusive and collectively exhaustive groups.

Step 2 is the select an independent random sample from each group.

33) When simple random samples are taken from each strata of a stratified sample based on

population proportions, it is called

a. simple stratified sampling

b. random stratified sampling

c. proportionate stratified sampling

d. probability proportionate to size sampling

Answer: C

By definition, it is a proportionate stratified sample. Probability proportionate to size is a

form of area sampling.

34) In disproportionate stratified sampling, more data should be collected from the strata cells

that

a. are the most homogeneous

b. are the most heterogeneous

c. have the smallest cell sizes

d. have the largest cell sizes

Answer: B

More data should be collected from cells with the higher variability, i.e. the most

heterogeneous.

35) The situation where a researcher directly selects groups and then uses all of the elements

in the groups is called

a. one-stage cluster sampling

b. two-stage area sampling

c. two-strata stratified sampling

d. one-stage systematic sampling

Answer: A

It is a one-stage cluster sample, because all of the elements are used within the groups that are

selected.

36) The situation where a researcher directly selects groups and then randomly selects

elements from within the selected groups is called

a. one-stage area sampling

b. two-stage cluster sampling

c. two-strata stratified sampling

d. two-stage systematic sampling

Answer: B

Stage one is the selection of the groups. Stage two is the random selection of the elements

within the selected groups.

37) In cluster sampling the groups should

a. be homogeneous

b. be heterogeneous

c. contain at least 30 cases

d. reduce the within-group variability

Answer: B

It is important in cluster sampling for the groups to be heterogeneous since each one should

reflect the population.

38) In _______________ sampling, the researcher selects every kth element in the frame,

after a random start somewhere within the first k elements.

a. random

b. systematic

c. area

d. stratified

Answer: B

By definition, systematic sampling selects every kth element.

39) The major problem with systematic sampling is _______________, which means that the

list of elements forming the sampling frame forms a cyclical pattern that coincides with a

multiple of the size of the sampling interval.

a. regularity

b. periodicity

c. multistaging

d. proportionality

Answer: B

This is the definition of periodicity, a possibility that can bias estimates in systematic

sampling.

40) All of the following methods of sampling require a complete and accurate list of the

elements of the population except

a. simple random sampling

b. stratified sampling

c. systematic sampling

d. area sampling

Answer: D

Area sampling can be performed without having a complete list of all elements within the

population.

SHORT ANSWER

1) How many sampling cells would be required for a quota sampling based on the following

control characteristics?

Age: 18 - 25, 26 - 40, 41 - 60, and 61+

Income: Less than $20,000, $20,000 - $39,999, and $40,000 - $59,999.

Education: Less than high school, High School, 2-year degree, and 4-year degree

Answer: 48 sampling cells

calculation: 4 × 3 × 4 = 48

2) For the following values, calculate the mean, variance, and standard deviation.

Data: 6, 8, 9, 12, 15

Answer: mean = 10

variance = 12.5

standard deviation = 3.54

calculation of mean:

50/5

calculation of variance:

s2 = SS/df

[(6 – 10)2 + (8 – 10)2 + (9 – 10)2 + (12 – 10)2 + (15 – 10)2] / 4 = 12.5

or using the computational formula:

[(36 + 64 + 81 + 144 + 225) – (50)2/5] / 4 = (550 – 500) / 4 = 12.5

calculation of standard deviation:

square root of 12.5

3) What is the relation of one, two, and three “standard errors” to the percent confidence

interval?

Answer: The confidence interval is always stated as the sample mean ± some number of

standard errors. Within one standard error of the sample mean is a 68 percent confidence

interval; two standard errors is a 95 percent confidence interval; three standard errors is a

99.7 percent confidence interval.

4) What are absolute and relative precision?

Answer: Absolute precision is the width of the confidence interval about a mean. Relative

precision is when the precision is expressed in percentages.

5) How does the within-sample variance differ between stratified sampling and cluster

sampling?

Answer: In stratified sampling, the samples are as homogenous as possible (low sample

variance), decreasing the overall sampling error. In cluster sampling, the samples are

designed to be as heterogeneous as the population (sample variance approaching that of the

population variance).

ESSAY

1) A properly defined population must be defined in what four terms? Give an example.

Answer: The four terms for properly defining a population are element, sampling unit, extent,

and time. An example is:

Element: purchasers of ACME widgets

Sampling units: supermarkets that carry ACME widgets, then purchasers

Extent: Boston

Time: Week of May 5 - 12

2) Outline the fives steps in selecting a sample.

Answer: Steps are:

1) Define the population by specifying the elements, the sampling units, the extent, and the

time frame.

2) Identify the sampling frame from which the sample will be selected.

3) Decide on a sample size, the total number of elements to include in the sample.

4) Select a specific procedure by which the sample will be determined.

5) Physically select the sample based on the procedure specified in step 4.

3) Discuss the constraints that affect sample size decisions.

Answer: Constraints include:

1) study objectives

2) time constraints

3) cost constraints

4) audience acceptability and politics

5) data analysis procedures

4) Explain the two primary ways a researcher can be assured that each element in an area

sample has an equal chance of being selected.

Answer: 1) Equal proportion selection of elements within clusters: With this method,

elements are selected based on the size of the clusters. For instance, if a cluster has twice as

many elements as another cluster, then twice as many elements would be selected.

2) Probability proportionate to size: With this method, each cluster is assigned a probability

based on its size relative to the other clusters and to the population as a whole. Thus, a large

cluster will have a greater chance of being selected than a small cluster.

5) Discuss the various implications of the central limit theorem to the practice of sampling.

Answer: The central limit theorem can be applied only when certain conditions hold during

probability sampling (it doesn’t hold for non-probability sampling methods). Among its

implications for sampling are:

• If the population distribution is normal, the sampling distribution of the mean will be

normal for all sample sizes.

• If the population distribution is not normal, the sampling distribution of the mean

approaches normality as the sample size increases.

• The mean of the sampling distribution (of the mean) is an unbiased estimate of the

population mean.

• The standard error of the sampling distribution (of the mean) is the population standard

deviation divided by the square root of the sample size.

Test Bank for Modern Marketing Research: Concepts, Methods, and Cases

Fred M. Feinberg, Thomas Kinnear, James R. Taylor

9781133188964, 9781133191025, 9780759391710