Chapter 12
Sample Size
sample size before collecting data?
a. quota sample
b. stratified sample
c. sequential sample
d. simple random sample
e. All sampling plans require an a priori determination of sample size.
statistic is
a. standard deviation.
b. variance.
c. standard error.
d. mean square error.
e. c and d.
a. the type of sample.
b. the statistic in question.
c. the homogeneity of the population.
d. a and c.
e. a, b, and c.
a population mean?
a. knowledge about or an estimate of the population variance
b. statement of the degree of precision desired
c. statement of the degree of confidence desired
d. b and c
e. a, b, and c
Consider the factors:
1. the standard error of the estimate
2. the desired precision of the estimate
3. the desired degree of confidence
4. the size of the population
a. 1,2
b. 2,3
c. 1,2,3
d. 2,3,4
e. 1,2,3,4
a. The particular sampling distribution of the statistic in question is of fundamental
importance in the determination of sample size. For example, the sampling
distribution of the sample means is used when estimating a population mean.
b. It is impossible to specify both the degree of confidence and the degree of
precision with a fixed size sample.
c. When determining the sample size necessary to estimate a population mean, it is
helpful to know the population variance, for if one knows the population variance,
he or she also knows the standard error of the mean up to a proportionality
constant.
d. a and c
e. a, b, and c are all true
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 the accuracy of the
estimate.
d. b and c are true statements.
e. A researcher should always use the most precise estimate.
a. increasing the confidence from 68% to 95% confidence
b. decreasing the confidence from 99% to 95% confidence
c. increasing the precision from 30 to 10
d. decreasing the precision from 10 to 40
e. increasing the precision from 5 to 10
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
of the characteristic in the population.
a. directly; variability
b. inversely; variability
c. inversely; size
d. directly; size
e. none of the above
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.
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. √6 million
e. 1 million
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
A researcher wishes to estimate the average annual expenditures per household on gasoline.
The estimate must be accurate within plus or minus $100 and the estimated standard deviation
in such expenditures is $500.
Use this problem to answer the following two questions.
a. 10.
b. 100.
c. 1000.
d. 5000.
e. not enough information given.
precision is 100 and the researcher wishes to be 95% confident in the result, the
required sample size is
a. 10.
b. 50.
c. 100.
d. 500.
e. none of the above.
mean with 95% confidence (z=2). The calculation of sample size required that he
estimate the population standard deviation since it was unknown, and he estimated
it as 150. The 100 observations produced a sample mean
_
x= ΣXi/n = 1000
and a sample standard deviation √ Σ (Xi-x)2/(n-1) = 200
The resulting confidence interval is
a. 970 < µ < 1030.
b. 996 < µ < 1004.
c. 997 < µ < 1003.
d. 960 < µ < 1040.
e. There are two possible confidence intervals.
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
a. relative precision.
b. absolute precision.
c. multiple precision.
d. statistical precision.
e. a and d.
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 if
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.
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.
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 .5
d. sample is greater than 5; population proportion is close to .9
e. the sample is greater than 30 but less than 100; the population proportion is close
to .1
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.
size required for a study to estimate a population proportion?
a. π =.1,z=3, and H=.01
b. π =.5,z=3, and H=.01
c. π =.1,z=1, and H=.01
d. π =.1,z=1, and H=.5
e. π =.5,z=1, and H=.5
Mary Marsh, head aerobic instructor at Tuff-it-Out Fitness Centers, wanted to estimate the
proportion of all 19-39 year olds who aerobically exercise at least once each week. Mary
would like the estimate to be within plus or minus 3 percentage points of the mean and she
would like to have 90 percent confidence (z=1.645) in her results. Use this information to
answer the next three questions.
a. 8.
b. 73.
c. 482.
d. 722.
e. 964.
desired. The required sample size is
a. 24.
b. 240.
c. 1,600.
d. 2,400.
e. 3,200.
researcher needed an estimate that was accurate within plus or minus 5 percent of the
population proportion. The required sample size is
a. 3.
b. 26.
c. 174.
d. 187.
e. 260.
sample to estimate it with a specified degree of precision and confidence?
a. .5
b. .4
c. .1
d. .9
e. 1.0
a. when the sample elements are dependent.
b. when the sample elements are independent.
c. when sample size represents less than 10 percent of the population.
d. always.
e. never.
following information:
a. variability of each strata.
b. cost per observation in each strata.
c. size of each strata.
d. a and b.
e. a, b, and c.
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