Deck 12: Sample Size Determination

Question 1

If we were making inferences from a single sample, we would expect that there would be a ____ percent probability that the sample mean or proportion generated from our sample results would be within two standard errors of the true population mean.

A) 68.26%
B) 99.74%
C) 97.5%
D) 95.44%
E) 98.00%

Answer 1

D

Question 2

The sample size is most often determined, indirectly by ___________________.

A) the number of respondents
B) the type of survey
C) the budget available
D) the sample size desired

Answer 2

B

Question 3

How many respondents should be in each important subgroup of a sample?

A) 10
B) 25
C) 50
D) 100

Answer 3

D

Question 4

The idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn, is known as:

A) sample variance.
B) population variance.
C) central limit theorem.
D) random error.
E) none of the above

Question 5

Higher levels of confidence generally require:

A) larger sample sizes.
B) greater variance.
C) smaller sample sizes.
D) smaller standard deviation.

Question 6

A researcher has been asked to determine if offering a discount drink during happy hour to those who purchase a drink in the morning increases the likelihood of their return in the afternoon, what statistic would he or she be most interested in?

A) variance
B) mean
C) standard deviation
D) proportion

Question 7

How can a researcher estimate the population standard deviation before selecting the sample?

A) use results from a prior survey
B) conduct a pilot survey
C) use secondary data
D) use judgment
E) all are ways to estimate standard deviation

Question 8

Researchers can determine via statistical techniques sample size. However, these techniques can only be applied to which of the following types of sample?

A) cluster
B) simple random
C) nonprobability
D) stratified
E) none of the above

Question 9

Which of the following is not a determinant of sample size for probability samples?

A) budget available
B) research objectives
C) rule of thumb
D) none of the above

Question 10

As the level of tolerable error increases in the sample means formula, the sample size required to represent a particular population is:

A) smaller.
B) larger.
C) about the same.
D) none of the above

Question 11

Which of the following statements about sample size is false?

A) There is no direct relationship between population size and the size of the sample required to estimate population parameters.
B) The larger the sample variance, the larger the sample size that is required.
C) The higher the level of confidence, the larger the sample size that is required.
D) The larger the population, the larger the sample size that is required.
E) All of the above statements are false.

Question 12

When a research company routinely uses samples of 300 for their studies, they are using which type of plan to determine sample size?

A) the 50% rule
B) budget available
C) rule of thumb
D) number of subgroups to be analyzed

Question 13

A researcher wants to know the average number of times per month respondents eat at fast food restaurants. The statistic that s/he is most interested in would be the_________.

A) variance
B) mean
C) standard deviation
D) proportion

Question 14

The assumptions that sample elements are drawn independently.

A) population standard deviation
B) allowable sampling error
C) independence assumption
D) sampling distribution

Question 15

The reasons a potential client may specify a sample size is based on____________.

A) the desired sampling error
B) a gut feeling
C) a pre-determined number
D) all of the above are reasons

Question 16

If it is important to analyze four subgroups of a total sample: married women over 35, single women over 35, married women under 35, and single women under 35 and each group is expected to make up about 25 percent of the total sample, a sample of 400 will only have 100 in each subgroup, what is the problem with the smaller sample size?

A) smaller groups lead to larger sampling errors
B) smaller groups lead to smaller sampling errors
C) larger total samples are needed for subgroups
D) none are problems with small sample sizes

Question 17

A normal distribution with a mean of zero and a standard deviation of one is a __________.

A) normal distribution.
B) chi-square distribution.
C) F-distribution.
D) mean distribution.
E) Standard normal distribution.

Question 18

Which of the following is not a piece of required information in order to determine sample size?
A) desired level of confidence

A) estimated population standard deviation
B) All are necessary to determine sample size.
B) estimated population median
C) acceptable level of sampling error

Question 19

A continuous distribution, which is bell-shaped and symmetric about the mean, is known as:

A) the normal distribution.
B) the chi-square distribution.
C) the F-distribution.
D) the mean distribution.
E) the binomial distribution.

Question 20

Holding constant at a 95% level of confidence, if the standard deviation increases, then the sample size required to represent the population in question will be _______.

A) larger
B) about the same
C) smaller
D) not applicable

Question 21

If large enough samples are taken, most human behavior can be plotted using a normal distribution curve.

Question 22

____________ is a range of values within which the true population value is estimated to fall.

A) Interval estimate
B) Point estimate
C) Population estimate
D) Sample estimate
E) none of the above

Question 23

A ____________ normal distribution is a normal distribution with a mean of zero and a standard deviation of one.

A) Balanced
B) Standard
C) Stock
D) Ordinary

Question 24

In a normal distribution, the mean, median, and mode are equal.

Question 25

Population size is the most important determinant of effective sample size.

Question 26

Which of the following is not a method for estimating the population standard deviation?

A) prior study results
B) conduct a pilot study
C) use secondary data
D) using population size

Question 27

Theoretically, the sampling distribution of the mean is always normally distributed.

Question 28

When a researcher is not sure if people who responded to the survey are different from those who did not respond, this brings into question the issue of:

A) inappropriate sample size.
B) systematic bias.
C) nonresponse bias.
D) refusal bias.

Question 29

Which of the following would increase the necessary sample size in a study?

A) smaller mean of the variables in question
B) less need for precision
C) need to divide sample into sub-groups
D) larger population
E) none of the above

Question 30

Which of the following is not a measure of central tendency?

A) variance
B) mean
C) median
D) mode

Question 31

Which of the following are not required to determine sample size using the sample means formula?
A) estimate of population standard deviation

A) the standard error of the mean
B) level of tolerable error
B) desired level of confidence
C) All of the above are required.

Question 32

A normal distribution has a total of 6 standard deviations.

Question 33

The greater the number of subgroups to be analyzed, the smaller the necessary sample size.

Question 34

Prior survey results can help a researcher estimate population standard deviation.

Question 35

___________ sampling error is the amount of sampling error the researcher is willing to accept.

A) Given
B) Projected
C) Accepted
D) Allowable

Question 36

Which of the following basic rules can help you calculate how many phone numbers are needed for a project?

A) the number of completed interviews needed
B) the working phone rate
C) the incidence rate
D) the contact and completion rate
E) all of the above

Question 37

About 68% of the area under a standard normal curve covers one _________.

A) mean
B) sample
C) variance
D) standard deviation
E) none of the above

Question 38

The normal distribution is bell shaped and has only one mode.

Question 39

The _____________ includes all the possible individuals or objects from whom or about which information is needed to meet the objectives of the research.

A) Group
B) Selection
C) Population
D) Range

Question 40

All of the statistical methods for determining sample size in this chapter assume which of the following?

A) a large population
B) a valid questionnaire
C) simple random sampling
D) stratified sampling
E) none of the above

Question 41

The finite population correction factor (FPC) is an adjustment to the required sample size that is made in cases where the sample is expected to be equal to 5 percent or more of the total population.

Question 42

Statistical power is the probability of making a type II error.

Question 43

Assuming the research objectives of the study can be accomplished, researchers would much prefer to estimate the required sample size using the sample proportion formula rather than the sample means formula. Why?

Question 44

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

Question 45

A researcher must be willing to allow for a certain amount of sampling error in any project.

Question 46

Compute the required sample size given the required confidence in the sample results is 90%. The level of tolerable sampling error is 1% and the estimated population standard deviation is 5.

Question 47

A type II error concludes that there is no difference when there is a difference.

Question 48

The total area under a normal curve is not equal to one, meaning all observations.

Question 49

A confidence interval always includes the true population value.

Question 50

Budget is rarely a consideration when determining sample size.

Question 51

The true population can only be found in the estimate range of values.

Question 52

Some normal distributions cannot be transformed into standard normal distributions.

Question 53

The "budget available" approach forces the researcher to explore alternative data-collection approaches and to carefully consider the value of information in relation to cost.

Question 54

A researcher is conferring with a client to do a telephone interview for a particular topic, which the researcher will subcontract to a field services firm for $10 per usable response. The researcher's client wants to be 95.44% confident of the results. Assume the sample proportions formula is appropriate, and that the level of tolerable sample error is 4%. The budget for data collection only offered by the client can be up to but not over $10,000. How many usable responses are needed for the given level of confidence and much will the subcontractor charge the market researcher for sampling? Is the budget for data collection large enough?

Question 55

The level of tolerable error (e) in the sample proportions formula is expressed in terms of a percent.

Question 56

If a researcher takes enough samples, the data will begin to approach a normal distribution.

Question 57

A range of values with which the true population value is estimated to fall is known as the point estimate.

Question 58

Subgroups are often chosen based on demographics of the sample, such as gender, income, etc.

Question 59

Determining sample size for probability samples involves managerial, financial, and statistical considerations.

Question 60

A type I error concludes that there is no difference when there is a difference.

Question 61

You wish to complete 300 phone interviews. Using a random-digit sample, you can expect your working phone rate will be only about 60 percent. How many calls will you likely have to make to achieve your desired interviews?

Question 62

A researcher wants to estimate a population mean. The level of tolerable sampling error is 0.2 of a purchase occasion, with a confidence level of 95.44%. If the estimated population variance is 5 for the most important question in the study, what is the desired sample size?

Question 63

A researcher wants to estimate the percentage of all adults that have used the Internet to seek pre-purchase information in the past 30 days, with a tolerable sampling error (E) of 0.03 and a confidence level of 97.5%. If secondary data indicated that 25% of all adults had used the Internet for such a purpose, what is the sample size?