Deck 10: Determining the Size of a Sample

Question 1

Sample accuracy refers to:

A)the extent to which the sample is validated.
B)the extent to which the sample statistics differ from the true population values the statistics represent.
C)the extent to which the population statistics differ from the representativeness of the sample.
D)a statistical concept that can be assessed only theoretically.
E)how close the sample statistics match the predetermined values expected by management.

Answer 1

B

Question 2

The sample size determines:

A)representativeness.
B)accuracy.
C)representativeness and accuracy.
D)the population statistic value.
E)the mean generated from the sample statistic.

Answer 2

B

Question 3

Which of the following is true regarding probability samples?

A)They are as perfect as a census and contain no errors caused by competitors.
B)They will always contain some inaccuracy (sample error).
C)They contain serious mistakes,but can be adjusted by statistical weighting procedures.
D)They are particularly susceptible to nonsampling errors.
E)When they approach large values,say 1,000,they are equivalent to a census.

Answer 3

B

Question 4

Which of the following is NOT a component needed for SSI's Formula for determining how many telephone numbers are needed?

A)incidence rate
B)completion rate
C)working phone rate
D)completed interviews required
E)number of qualified interviewers

Question 5

Which of the following statements is most accurate regarding the relationship between sample size and the sample representativeness?

A)There is a high relationship between the size of a sample and the representativeness of the population from which it is drawn.
B)There is no relation between the size of a sample and the representativeness of the population from which it is drawn.
C)You cannot have a representative sample unless the sample size is equal to or exceeds 10 percent of the population.
D)Sample size determines representativeness but only if the sample plan is a probability sampling plan.
E)Sample size determines representativeness but only if the sample plan is a nonprobability sampling plan.

Question 6

Which of the following would be defined as the percentage of respondents that qualify for a survey based on criteria such as age,income,and race?

A)demographic incidence
B)geographic incidence
C)demographic occurrence
D)product incidence
E)customer data

Question 7

Which of the following is NOT one of the axioms of sample size and accuracy?

A)The only perfectly accurate sample is a census.
B)A probability sample will always have some inaccuracy (sample error).
C)Increasing sample size increases the sample's representativeness.
D)A probability sample size can be a very tiny percentage of the population size and still be very accurate.
E)The size of a probability sample depends on the client's desired accuracy balanced against the cost of data collection.

Question 8

Unfortunately,many managers falsely believe that sample size is:

A)related to proper data analysis.
B)related to the representativeness of the sample.
C)determined by computer programs.
D)an irrelevant "statistical" technicality issue.
E)related to the level of accuracy desired.

Question 9

Sources of error that come from sources other than the sample selection method and sample size are referred to as:

A)serious mistakes.
B)nonsampling errors.
C)errors caused by competitors.
D)errors caused by clients.
E)errors caused by statisticians.

Question 10

In a study of the U.S.workforce population,a research company interviews 5,000 persons on a street corner in New York.If they decide to increase the sample size to 10,000,they would:

A)increase the sample size and the representativeness of the sample.
B)increase both sample accuracy and representativeness of the sample.
C)increase only the representativeness.
D)decrease the sample accuracy.
E)increase the sample size,but the sample would still not be representative of the population.

Question 11

Consider that we have nominal data (responses are categorical)and the responses are "Yes" or "No" to the question: "The next time you order pizza,will you use Domino's?" Which of the following sets of responses shows the MOST variability?

A)90 percent say "Yes" and 10 percent say "No"
B)80 percent say "Yes" and 20 percent say "No"
C)70 percent say "Yes" and 30 percent say "No"
D)60 percent say "Yes" and 40 percent say "No"
E)55 percent say "Yes" and 45 percent say "No"

Question 12

Which of the following is true with regard to variability?

A)p is always less than q
B)q is always less than p
C)q=100%-p
D)p and q are always equal
E)p+q=1.96

Question 13

Which of the following is true regarding a probability sample?

A)The larger the sample size,the more likely the sample is representative.
B)The larger the sample size,the more accurate it is (less sample error).
C)The more representative the sample,the larger the sample size.
D)They only become accurate when they are larger than 1,000.
E)The larger the sample size,the more room there is for inaccuracy.

Question 14

One of the reasons why a marketing practitioner should have a basic understanding of sample size determination is because:

A)many practitioners have a false belief that sample size doesn't determine a sample's representativeness.
B)it helps managers to manage their resources better.
C)a marketing manager should understand that a sample's representativeness is not related to its accuracy.
D)the size of the sample is never a major cost factor.
E)managers always have a "small sample bias";they believe small samples are more accurate.

Question 15

If you were to graph sample accuracy and sample size,which of the following generalizations would be most accurate?

A)Accuracy is very low,even with small sample sizes of 50 or below.
B)Accuracy constantly increases as sample size increases;a sample of 2,000 is four times more accurate than a sample of 500.
C)With increases in sample size,sample accuracy decreases.
D)We cannot graph sample size and accuracy because we must also include the level of confidence and the variability within the sample data.
E)Accuracy increases rapidly when sample size increases up to about 500 and then levels off.

Question 16

If we were to graph the relationship of sample size (x axis)to sample accuracy (y axis),we would notice that:

A)there is a linear relationship between size and accuracy.
B)accuracy increases quickly,up to about sample size 500,and then accuracy levels off with relatively small gains made even when sample size is increased to as much as 2,000.
C)accuracy increases quickly,up to about sample size 5,000,and then accuracy levels off with relatively small gains made even when sample size is increased to as much as 200,000.
D)accuracy increases quickly,up to about sample size 50,and then accuracy levels off with relatively small gains made even when sample size is increased to as much as 100.
E)We cannot graph sample size and accuracy because we must also include the level of confidence and the variability within the sample data.

Question 17

If we know the level of confidence (1.96 for 95 percent),variability estimates,and the size of a sample,there is a formula that allows us to determine:

A)the costs of the sample.
B)the size of the sample.
C)the representativeness of the sample.
D)p or q.
E)the accuracy (sample error).

Question 18

When all other factors are held constant,as we increase the level of accuracy,the sample size and the cost of a marketing research survey are best characterized by which of the following?

A)The sample size will increase but the cost will decrease.
B)The sample size will decrease but the cost will increase.
C)The sample size and the cost of the survey will increase.
D)The sample size will remain the same but the cost will increase.
E)The sample size will decrease but the cost will remain the same.

Question 19

Which of the following is the best definition of variability?

A)It is the amount of dispersion in a data set containing interval or nominal data.
B)It is the difference between scores in the present sample and scores in a previous sample.
C)It is the amount of dissimilarity in ordinal data.
D)It is the amount of dissimilarity (or similarity)in respondents' answers to a particular question.
E)It is the amount of responses in one respondent's answers to a particular survey question.

Question 20

Which of the following is the most correct method of determining sample size?

A)percentage of population approach
B)all that can be afforded approach
C)all that time will permit approach
D)using the "100" for local study;"1,000" for national study approach
E)the confidence interval approach

Question 21

What three factors are needed to calculate sample size?

A)variability,accuracy,and confidence level
B)variability,accuracy,and population size
C)accuracy,confidence level,and population size
D)accuracy,population size,and costs
E)variance,standard deviation,and dispersion

Question 22

Level of confidence in sample size formulae is normally set at:

A)95 percent or 96 percent.
B)5 percent or 10 percent.
C)95 percent or 99 percent.
D)1 percent or 5 percent.
E)None of the above;level of confidence is determined by the formula.

Question 23

When determining sample size,the conventional approach would NOT be:

A)an average of the sample sizes of similar studies.
B)the modal sample size of previous surveys.
C)5 percent of the entire population.
D)the sample size of a competitor's survey that the company somehow discovered.
E)the sample sizes normally reported in published reports.

Question 24

If we are using the formula for calculating the sample size for estimating a mean,the formula will contain:

A)s)
B)%)
C)Z3.
D)pq.
E)None of the above;there is no sample size formula for estimating a mean.

Question 25

When attempting to balance the sample size with the cost of data collection,the textbook illustrated that it is helpful to:

A)use an Excel spreadsheet.
B)rely on financial leveraging.
C)use a table that depicts data collection cost and sample error for different sample sizes.
D)use a table that depicts data collection cost and the costs of computing different sample sizes.
E)use a table that depicts data collection cost contrasted to the cost of not doing research.

Question 26

Which of the following is the theory that allows us to say that if we conducted a survey 1,000 times,and we were to plot the answers to our survey,the plot would appear as a normal curve?

A)the central limit theorem
B)the normal curve theory
C)the normal limit theorem
D)the confidence interval theorem
E)the variability coefficient theory

Question 27

95 percent of the observations under the normal curve fall within ________ times the sample error.

A)±1.64
B)±1.96
C)±2.58
D)±95
E)±1.95

Question 28

A sample that has been determined by using a cost basis approach would be when:

A)the manager has discussed the statistical analysis with the research project director.
B)the manager has discussed the competitor's marketing results with the research project director.
C)the manager has discussed the previous marketing study with the research project director.
D)the manager has discussed the budget with the research project director and they have decided to spend "all they can afford" on the project.
E)none of the above

Question 29

If you were conducting a telephone survey of households using random digit dialing numbers and you determined that you needed a sample size of 1,100,which of the following would be most accurate?

A)You would need to obtain exactly 1,100 telephone numbers to call.
B)You would need to obtain far less than 1,100 telephone numbers because you know that many will not answer or cooperate anyway.
C)You will need some multiple of the 1,100 numbers in order to ensure you account for factors such as numbers that are for business phones,ineligible households (incidence rate),and those numbers dialed whose owners refuse to participate.
D)You will need only a few extra numbers to allow for those who have moved away.
E)You start off with 1,100;there is no way to determine approximately how many numbers you will actually need.

Question 30

Which of the following statements best illustrates the concept of the "level of confidence" or z value chosen in sample size formulae?

A)By setting z at 1.96 it means that the manager could expect,if she conducted the survey many,many times,the value of p would fall within the sample error range 95 percent of the time.
B)By setting z at 1.96 it means that the manager could expect,if she conducted the survey many,many times,the value of p would fall within the sample error range 5 percent of the time.
C)By setting z at 2.58 it means that the manager could expect,if she conducted the survey many,many times,the value of p would fall within the sample error range 95 percent of the time.
D)By setting z at 1.96 it means that the manager could expect,if she conducted the survey many,many times,the value of p would fall within the sample error range 99 percent of the time.
E)By setting z at 2.58 it means that the manager could expect,if she conducted the survey many,many times,the value of p would fall within the sample error range 1 percent of the time.

Question 31

In sample size formulas,the symbol "e" stands for:

A)estimated parameter or desired confidence level.
B)acceptable population equation.
C)estimated statistic or desired variability.
D)estimated confidence interval.
E)acceptable sample error.

Question 32

The only time the population size is important in the calculation of sample size is:

A)always;all formulas include N,a count of the total population.
B)when the population is very,very large.
C)when the population is not normal.
D)when the level of accuracy needs to be less than ±5 percent.
E)when the population is small,relative to the sample size.

Question 33

National opinion polls tend to use sample sizes ranging from:

A)10 to 100
B)1,000 to 1,200
C)50,000 to 100,000
D)1 million to 5 million
E)10 million to 15 million

Question 34

If we are using the formula for calculating the sample size for estimating a percentage,the formula will contain:

A)s)
B)%)
C)Z3.
D)pq.
E)N)

Question 35

If we are using the sample size formula to be used when estimating a mean and we are trying to determine e,we are trying to indicate:

A)the allowable error.
B)the proportion of s to S in the sample.
C)the range of possible z scores in the population.
D)the percentage of the respondents who will answer p.
E)the percentage of the respondents who will answer q.

Question 36

The basic difference between an arbitrary and a conventional sample size determination is that:

A)the conventional approach has no defensible logic,whereas the arbitrary approach appears to have faulty logic.
B)the conventional approach doesn't appear to be logical,whereas the arbitrary approach has defensible logic.
C)the arbitrary approach has no defensible logic,whereas the conventional approach is logical.
D)the arbitrary approach has no defensible logic,whereas the conventional approach appears logical but is faulty.
E)the arbitrary approach,though arbitrary,has sound logic,and the conventional approach has conventional support.

Question 37

In trying to estimate the variability in the population in order to determine pq,which of the following represents viable alternatives?

A)Use a random number generator to provide two random values for p and q.
B)Use the most conservative approach,p = 10,q = 90.
C)Use 90/10 or find a former study and calculate the variance or conduct a pilot study.
D)Use 1/5 or find a former study and calculate the variance or conduct a pilot study.
E)Use 50/50 or find a former study and calculate the variance or conduct a pilot study.

Question 38

Sample size is related to the size of the confidence interval in that:

A)the larger the sample size,the larger the confidence interval.
B)the larger the sample size,the more normal the confidence interval.
C)the smaller the sample size,the smaller the confidence interval.
D)the smaller the sample size,the more uniform the confidence interval.
E)the larger the sample size,the smaller the confidence interval.

Question 39

If we assume the "highest" amount of variability when estimating pq,then pq are:

A)50,50.
B)1,99.
C)0,10.
D)1,5.
E)0,5.

Question 40

If we are using the sample size formula to be used when estimating a mean and we are trying to determine s,we are trying to indicate:

A)the pq population mean.
B)the variability in the population represented by the standard deviation.
C)the sample size.
D)the allowable error represented by the standard deviation.
E)None of the above;the formula does not have an s.

Question 41

The sample size is always related to how representative the sample is of the population.

Question 42

Sampling error is the difference between the sample findings and the findings that the client expected to have prior to the survey.

Question 43

Variability is defined as the amount of dissimilarity or similarity in respondents' answers to a particular question.

Question 44

Sample size has a direct bearing on how accurate the sample's findings are relative to the true values in the population.

Question 45

Instead of determining representativeness,the size of the sample affects the sample accuracy of the results.

Question 46

A graph of the relationship between accuracy and size of the sample shows that accuracy decreases as sample size increases.

Question 47

The only perfectly accurate sample is a census.

Question 48

You are going to use a purposive sample (a nonprobability sample)to collect data from fast-food restaurant customers.Which of the following concepts would be applicable to determining sample size?

A)confidence intervals
B)sample size formula for estimating a percentage
C)sample size formula for estimating a mean
D)estimating a population value within a stated percent of allowable error
E)None of the above would be appropriate;sample size concepts and formulas are only applicable when probability sampling plans have been used.

Question 49

Nonsampling error pertains to all sources of error other than the sample selection method and sample size.

Question 50

Which of the following samples have been determined by using the statistical analysis approach?

A)the sample size needed to properly analyze subgroups
B)1,000 respondents
C)between 1,000 and 1,200 respondents
D)200 respondents because each interview is $30
E)a former study's sample,which generated favorable statistics

Question 51

Sample size does not have to be "huge" in order to have reasonably accurate data.For example,samples that are 400 or less may provide reasonably accurate information.

Question 52

A random sample must be perfectly accurate to be considered a very good representation of the population.

Question 53

By applying the finite multiplier it is possible to:

A)reduce the population and achieve the same accuracy level.
B)reduce the sample size or achieve the appropriate accuracy level.
C)reduce the sample size and achieve the same accuracy level.
D)reduce the accuracy level and maintain the same sample size.
E)None of the above;there is no "finite multiplier."

Question 54

A finite multiplier is used when the population,relative to the sample size,is:

A)small.
B)large.
C)finite.
D)variable.
E)infinite.

Question 55

The confidence interval approach to determining sample size applies the concepts of accuracy,variability,and confidence interval to create a "correct" sample size.

Question 56

A graph of the relationship between accuracy and size of the sample shows that accuracy increases dramatically up until sample sizes near 500.Thereafter,it takes much larger increases in sample size to gain increases in accuracy.

Question 57

Sample accuracy refers to how close a random sample's statistic is to another random sample statistic drawn on the same population.If the two samples result in the same,or nearly the same,data,then one has achieved sample accuracy.

Question 58

The size of a probability sample depends on the client's desired accuracy (acceptable sample error)balanced against the cost of data collection for that sample size.

Question 59

Sample error may only be determined after data have been collected.Even if we know the level of confidence,an estimate of variability (p∗q)and the sample size,n,we cannot compute the amount of sample error we can expect to experience.

Question 60

Large sample size bias refers to a belief that sample size determines a sample's representativeness.

Question 61

In determining the level of confidence,any level of confidence is possible,but marketing researchers typically use between 60 percent and 100 percent ,depending on the importance of the issue and how much the client has to spend on the research.

Question 62

If you calculate sample size with an e of 3 percent,and then you decide to change e to 5 percent,the required sample size will go up.

Question 63

With the 99% level of confidence,the corresponding z value is 2.58.

Question 64

Using the confidence interval formula for calculating sample size,the amount of variability believed to be in the population must be estimated.

Question 65

The arbitrary approach to sample size determination takes the desired level of accuracy into account.

Question 66

Variability (standard deviation)of a population where a mean is being estimated may be estimated by dividing the range by 6.

Question 67

The basic concept of the central limit theorem is that all research findings are limited in their application simply because they are based upon a sample and not a census.

Question 68

It is almost always up to the researcher to educate the manager on what might be acceptable or "standard" sample error.

Question 69

In a "Yes/No" question,50 percent "Yes" and 50 percent "No" shows less variability than does 90 percent "Yes" and 10 percent "No."

Question 70

Researchers should follow to the sample size formula closely when calculating sample size.No other consideration,such as the cost to the client,should be considered,as it will surely lower the accuracy of the study.

Question 71

In sample size formulae,acceptable sample error is noted by "e."

Question 72

Using the confidence interval formula for calculating sample size,the level of confidence desired to the estimate of the population values must be determined and is represented in the formula by the z value.

Question 73

The desired accuracy should NOT be considered in order to calculate the proper sample size.This is because accuracy cannot be determined until the data are collected and analyzed.

Question 74

The axiom,"You can take any finding in the survey,replicate the survey with the same probability sample size,and you will be very likely to find the same finding within the ± percent range of the original finding," is based on the idea of the confidence interval.

Question 75

A probability sample size can be a very tiny percent of the population size and still be very accurate (have little sample error).

Question 76

There is a separate sample size formula for estimating a percentage of the population than for estimating a mean of the population.

Question 77

The only time that the population size is a consideration in sample size determination is in the case of a "small population."

Question 78

The conventional approach to sample size determination follows some convention or number believed somehow to be the "correct" sample size.

Question 79

The most significant factor in calculating sample size (n)is the size of the population (N).For example,if you calculated that you needed a sample size of 300 in order to have an accurate sample for your hometown,it would take at least 10 times this amount,or about 3,000,in order to have an accurate sample representing the entire United States.

Question 80

It is "true" to say that,in practice,you can estimate variability in the population by using one of three methods: (a)set pq to the most conservative amounts of 50 percent/50 percent, (b)estimate pq based upon prior research studies,or (c)conduct a pilot study.