Deck 16: Determining Sample Size

Question 1

Exhibit 16.2 A researcher wishes to estimate the average annual expenditures per household on gasoline.The estimate must be accurate within plus or minus $50 and the estimated standard deviation for such expenditures is $400.
Refer to Exhibit 16.2.For a 95%-confidence interval (use z = 2),the required sample size is

A)250.
B)128.
C)256.
D)640.
E)Not enough information given.

Answer 1

C

Question 2

Exhibit 16.3 Stella would like to determine the amount of the average purchase at her software store with a total precision of $10,a historical average purchase variance of $150,and at a 95% confidence level.
Refer to Exhibit 16.3.What sample size does Stella need?

A)2
B)12
C)24
D)30
E)8

Answer 2

C

Question 3

If the desired level of confidence to estimate a mean is increased from 90% (with z = 1.60)to 95%,the sample size is increased by a factor of ____,all else equal.

A)2.50
B)4.65
C)Has no effect on sample size.
D)1.56
E)2.00

Answer 3

D

Question 4

Which of the following sampling plans does NOT require determining the necessary sample size before collecting data?

A)Quota sample
B)Stratified sample
C)Sequential sample
D)Simple random sample
E)All sampling plans require prior determination of sample size.

Question 5

Exhibit 16.3 Stella would like to determine the amount of the average purchase at her software store with a total precision of $10,a historical average purchase variance of $150,and at a 95% confidence level.
Refer to Exhibit 16.3.If Stella wishes to increase the total precision to $5,what sample size is needed?

A)8
B)54
C)48
D)96
E)24

Question 6

Sample size depends upon the

A)type of sample.
B)statistic in question.
C)homogeneity of the population.
D)Both a and c.
E)a,b,and c.

Question 7

Toppen Olaf Olson,plant manager at the Ridgway Tanning Factory,was interested in the average number of hides currently sold each day at the plant.The daily variance of hides sold at the plant last year was 132.Olaf would like to be 90 percent confident (z = 1.645)in his results and be within a daily range of +/- 5 hides.Olaf needs a sample of what size to achieve his desired level of precision and confidence?

A)15
B)22
C)472
D)1,886
E)2,788

Question 8

The size of the sample required to estimate a population mean is ____ proportional to the ____ of the characteristic in the population.

A)directly,variability
B)inversely,variability
C)inversely,size
D)directly,size
E)uniformly,size

Question 9

Which of the following are required to determine the sample size necessary to estimate a population mean?

A)Knowledge about or an estimate of the population variance
B)A statement of the degree of precision desired
C)A statement of the degree of confidence desired
D)Both b and c.
E)a,b,and c.

Question 10

There is a trade-off between the confidence level and the degree of precision of the estimate when the

A)population is finite.
B)sample size is fixed.
C)sample size varies.
D)population is infinite.
E)sample size is small.

Question 11

The error associated with the estimation of a population parameter from a sample statistic is

A)standard deviation
B)variance
C)standard error
D)mean square error.
E)Both c and d.

Question 12

Suppose that the income of the population of the city of Seattle is normally distributed and varies approximately from 0 to 6 million;what is the estimated standard deviation?

A)Insufficient information to estimate
B)2 million
C)3 million
D)square root of 6 million
E)1 million

Question 13

A researcher is attempting to determine the average annual expenditures per household on albums.Suppose $300 was considered the upper limit and $0 the lower limit.There are no past studies on which to base an estimate of s.What is your best estimate of the standard deviation?

A)$0
B)$50
C)$150
D)$300
E)No way to determine.

Question 14

If the desired precision to estimate a mean is increased by a factor of four (for example,from 40 to 10)the sample size is increased by a factor of ____,all else equal.

A)30.0
B)4.0
C)16.0
D)2.0
E)32.0

Question 15

Exhibit 16.2 A researcher wishes to estimate the average annual expenditures per household on gasoline.The estimate must be accurate within plus or minus $50 and the estimated standard deviation for such expenditures is $400.
Refer to Exhibit 16.2.Given estimates and specifications that the population standard deviation is $200,TOTAL precision is $100 and the researcher wishes to be 95% confident in the result,the required sample size is

A)42.
B)32.
C)16.
D)64.
E)Not enough information given.

Question 16

Which of the following is(are)a valid reason(s)why a researcher might not want to increase the precision of the estimate?

A)It would increase the standard error.
B)It would increase the required sample size.
C)It could produce a reduction in confidence with respect to accuracy of the estimate.
D)Both b and c.
E)A researcher should always use the most precise estimate.

Question 17

Exhibit 16.1 Refer to Exhibit 16.1.Which of these factors does one need to consider when estimating sample size?

A)1,2
B)2,3
C)1,2,3
D)2,3,4
E)1,2,3,4

Question 18

If a researcher wishes to increase the confidence level from 95% to 99%,what approximately will be the effect on sample size?

A)The sample size will decrease in proportion to the increase in the confidence level.
B)The ratio of the new sample size to the old is 3/2.
C)The ratio of the new sample size to the old is 2/3.
D)The ratio of the new sample size to the old is 9/4.
E)The ratio of the new sample size to the old is 4/9.

Question 19

Two standard deviations about the mean of a normal distribution include approximately ____ of all observations.

A)90%
B)95%
C)99%
D)Can't say;it depends on the individual sample variance.
E)Can't say;it depends on the size of the population.

Question 20

Which of the following is NOT an acceptable method of estimating the population standard deviation?

A)Perform a pilot study.
B)Divide the estimated range of variation by 2.
C)Use an estimate based on past studies of the same phenomenon.
D)Divide the estimated range of variation by 6.
E)Use an estimate based on the method used to measure the important variables.

Question 21

Which of the following estimated population proportions would require the largest size sample to estimate it with a specified degree of precision and confidence?

A)0.50
B)0.40
C)0.10
D)0.90
E)1.00

Question 22

A researcher was conducting an investigation to determine if level of education affected a person's consumption of alcoholic beverages.The researcher was specifically interested in determining whether those with a grade school,high school,or college education were more likely to drink beer,wine,or hard liquor.To investigate the question the researcher planned to cross-classify these three education levels of respondents against their preferences for each of these beverages.She estimated that 20 percent of the population of interest had a college education,70 percent a high school education,and 10 percent only a grade school education,and further that 40 percent of the population preferred beer,40 percent wine,and 20 percent hard liquor.She desired a minimum of 20 observations per cell on which to base percentages.How large a sample should she select?

A)200
B)250
C)400
D)500
E)100

Question 23

A researcher determined the size sample necessary to estimate two population means Y and Z.The indicated sizes were 200 to estimate Y and 300 to estimate Z with the specified degrees of confidence and precision.The researcher decided therefore to use a sample of size 250.Assuming the estimates of the population standard deviation were correct

A)the estimate of Y is more precise than desired while that for Z is less precise than desired.
B)the estimate of Y is less precise than desired while that for Z is more precise than desired.
C)Y is estimated with exactly the specified degree of precision while Z is estimated less precisely than desired.
D)Z is estimated with exactly the specified degree of precision while Y is estimated less precisely than desired.
E)Both Y and Z are estimated with the exact specified degree of precision.

Question 24

Exhibit 16.4 A researcher is attempting to determine the average annual expenditures per household on compact discs.Suppose $600 was considered the upper limit and $0 the lower limit.There are no past studies on which to base an estimate of s.
Refer to Exhibit 16.4.What is your best estimate of the standard deviation?

A)$120
B)$200
C)$100
D)$300
E)No way to determine.

Question 25

A soap manufacturer wants to know within +4 percentage points what percentage of households use liquid soaps.To be 95% confident in the estimate,how many households should be sampled? (Note: a confidence interval greater than +4 percentage points is unacceptable. )

A)600
B)625
C)700
D)750
E)550

Question 26

The normal distribution most closely approximates the binomial when ____ and ____.

A)the sample is small,population proportion is small
B)the sample is large,population proportion is small
C)the sample is large,population proportion is close to 0.5
D)sample is greater than 5,population proportion is close to 0.9
E)the sample is greater than 30 but less than 100,the population proportion is close to 0.1

Question 27

A researcher estimated an unknown population standard deviation to be 150.Using a sample of size n = 135,the sample standard deviation was found to be 100.The researcher now wishes to establish a 95% confidence interval for the population mean.Which of the following is the correct standard error of the mean to use in calculating the desired confidence interval?

A)Can't be determined from the information given.
B)1.05
C)12.91
D)0.86
E)8.61

Question 28

Exhibit 16.5 A researcher wished to estimate the proportion of all families who go to the movies at least once a month.He wished the estimate to be accurate within plus or minus 4 percentage points and further desired a 95 percent confidence interval (z = 2)around the result.Additionally,he estimates the population proportion as 0.30.
Refer to Exhibit 16.5.After the households were surveyed,the sample proportion of households using liquid soap was determined to be 0.2.The precision at the 95% confidence level is + or -

A)0.028 percentage points.
B)0.032 percentage points.
C)0.040 percentage points.
D)0.057 percentage points.
E)0.141 percentage points.

Question 29

In the absence of any information concerning the population proportion the conservative researcher should use which of the following estimates when calculating sample size?

A)1.00
B)0.20
C)0.50
D)0.80
E)0.00

Question 30

Exhibit 16.5 A researcher wished to estimate the proportion of all families who go to the movies at least once a month.He wished the estimate to be accurate within plus or minus 4 percentage points and further desired a 95 percent confidence interval (z = 2)around the result.Additionally,he estimates the population proportion as 0.30.
Refer to Exhibit 16.5.The required sample size is

A)24.
B)525.
C)300.
D)600.
E)575.

Question 31

When using anticipated cross classifications to determine sample size,the general "rule of thumb" suggests using at least ____ units in major breakdowns and ____ units in minor breakdowns.

A)150,20 to 50
B)50,10 to 20
C)75,100
D)200,75
E)100,20 to 50

Question 32

Exhibit 16.4 A researcher is attempting to determine the average annual expenditures per household on compact discs.Suppose $600 was considered the upper limit and $0 the lower limit.There are no past studies on which to base an estimate of s.
Refer to Exhibit 16.4.If the desired precision is +$25 and the desired confidence interval is 95%,what is the necessary sample size?

A)240
B)540
C)92
D)64
E)None of the above.

Question 33

Exhibit 16.5 A researcher wished to estimate the proportion of all families who go to the movies at least once a month.He wished the estimate to be accurate within plus or minus 4 percentage points and further desired a 95 percent confidence interval (z = 2)around the result.Additionally,he estimates the population proportion as 0.30.
Refer to Exhibit 16.5.Suppose that a 99 percent confidence interval (z = 3)were desired.The required sample size is

A)54.
B)450.
C)1381.
D)1181.
E)1000.

Question 34

When estimating a population proportion instead of a mean,in order to determine the sample size necessary you need all of the following information EXCEPT

A)degree of confidence.
B)estimate of the proportion.
C)estimate of the heterogeneity of the population.
D)specified precision.
E)All of the above are necessary items of information.

Question 35

A researcher has estimated that she needs a sample of size n=100 from a population consisting of 1,000 elements.Recognizing that the sample represents 10% of the population,she decides to apply the finite population correction factor to her initial estimate.What is the corrected sample size?

A)10
B)84
C)105
D)91
E)95

Question 36

is the

A)proportion of successes in n trials.
B)level of precision.
C)standard error of the proportion.
D)unbiased estimate of the population proportion.
E)standard error of the mean.

Question 37

The finite population correction factor

A)is used when the sample size is larger than 5 percent of the population.
B)reduces the estimate of the standard error.
C)can be used to decrease the costs of a study.
D)Both a and b.
E)a,b,and c.

Question 38

If the estimated range of incomes for 30 medium size businesses is $60,000,a rough estimate of one standard deviation would be

A)$10,000.
B)$12,000.
C)$8,000.
D)$8,500.
E)$9,000.

Question 39

If the sample standard deviation turns out to be larger than the estimated population standard deviation,the confidence interval to estimate a population mean will be ____ planned.

A)Narrower than
B)Wider than
C)The same as
D)As precise as
E)None of the above

Question 40

The finite population correction factor is used when

A)the sample elements are dependent.
B)the sample elements are independent.
C)sample size represents less than 10% of the population.
D)always.
E)never.

Question 41

The degree of error in a study,or the size of the estimating interval is called ____________________.

Question 42

In estimating the standard deviation in the population for the formula for calculating the sample size for estimating a mean,we can use some prior knowledge about the

A)sample to estimate our standard deviation.
B)population,undertake a pilot study or estimate the range,and divide by 10.
C)population,undertake a pilot study or estimate the range,and divide by 6.
D)Either of the two;b or c would work.
E)None of the above;if you do not have the actual standard deviation,you cannot use the formula.

Question 43

What three factors are needed to calculate sample size?

A)Variability,precision,and confidence.
B)Variability,precision,and population size.
C)Precision,confidence,and population size.
D)Precision,population size,and costs.
E)None of the above.

Question 44

A study is to be performed for a local restaurant.The owner wants to know the awareness of the restaurant name as well as satisfaction with food,service,and prices.Furthermore,he wants to know answers to the above issues by subgroups such as those who have eaten lunch meals,dinner meals,weekday patrons,and weekend patrons.Since the sample size formula cannot be used,the study should arbitrarily decide to sample 100 patrons per subgroup

Question 45

Choosing a sample of size n at random is statistically equivalent to first identifying all possible samples of size n in the population and then picking one of these samples randomly.

Question 46

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 (all else being equal)?

A)90% say "Yes" and 10% say "No"
B)80% say "Yes" and 20% say "No"
C)70% say "Yes" and 30% say "No"
D)60% say "Yes" and 40% say "No"
E)50% say "Yes" and 50% say "No"

Question 47

In a study of the U.S.labor force to determine its attitudes and opinions,a research company interviews 5,000 persons on a street corner in Manhattan,NY.In order to get more accurate results,they decide to increase the sample size to 10,000.Which of the following would be true?

A)Increase the sample size will increase the representativeness of the sample.
B)Increase the sample size would still not increase the representative of the sample.
C)Since a convenient sample was used,sample representativeness is impossible.
D)Both b and c.
E)None of the above is correct.

Question 48

The only time the population size (N)is important in the calculation of sample size (n)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 population is small relative to the sample size.
E)None of the above.

Question 49

These three factors are needed to calculate sample size: ____________________,____________________,and ____________________.

Question 50

It is only when sample size is allowed to vary that it is possible to achieve given levels of both precision and confidence.

Question 51

People who have looked online for health information are called "____________________."

Question 52

The standard error will increase if sample size is increased.

Question 53

When the sample size will represent more than 5-10% of the population,the calculated sample size should be increased by the finite population correction factor.

Question 54

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

A)There is no relation between the size of a sample and the representativeness of the population from which it is drawn.
B)There is a strong positive relationship 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 ten percent of the population.
D)Sample size determines representativeness but only if the sample plan is a probability sampling plan.
E)None of the above.

Question 55

"Cyberchondriacs" is a term used for people who have looked online for health information.

Question 56

If you were to graph precision (H)and sample size (n),which of the following generalizations would be most accurate?

A)Precision is very low with small sample sizes of 50 or below.
B)Precision constantly increases as sample size increases;a sample of 2,000 is four times more precise than a sample of 500.
C)Precision increases rapidly when sample size increases up to about 500 and then begins to level off.
D)Precision and sample size have nothing to do with each other,therefore graphing them make no sense
E)Both b and c are true.

Question 57

The degree of homogeneity in the population,on the characteristic to be estimated,directly influences sample size.

Question 58

Each stage of the research process is interrelated and research teams should consider the entire process before undertaking any data collection.

Question 59

Sample size (n)is related to the degree of the confidence (1-alpha)in that the

A)larger the degree of confidence,the larger the sample size.
B)smaller the degree of confidence,he larger the sample size.
C)sample size would be the same irrespective of the degree of confidence.
D)sample size formula is related to z and not to the degree f confidence.
E)None of the above.

Question 60

Precision refers to the degree to which one can feel confident that an estimate approximates the true value.

Question 61

____________________ is the degree to which one can feel confident that an estimate approximates the true value.

Question 62

Discuss three factors researchers must take into consideration when determining sample size.

Question 63

It is only when sample size is allowed to vary that it is possible to achieve given levels of both ____________________ and ____________________.