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Chapter 16
Data Analysis: Examination of Differences
observed pattern of frequencies corresponds to the expected pattern. The appropriate
statistical technique is
a. Chi-square contingency table analysis.
b. Kolmogorov-Smirnov test.
c. z-test for one mean.
d. z-test for two means.
e. none of the above.
of freedom?
a. Chi-square
b. F-test
c. Kolmogorov-Smirnov
d. normal distribution
e. all nonparametric distributions
expected pattern. Which test is appropriate in this situation?
a. a t-test if there are less than 30 observations and a z-test if there are more than 30
observations
b. Kolmogorov-Smirnov test
c. Chi-square goodness-of-fit test
d. F-test
e. None of the above is appropriate.
of the following formulas are used to calculate the test statistic?
_
a. z = x-µ
σ_
x
_
b. t = x-µ
σ_
x
_
c. z = x-µ
s_
x
_____________
n _
d. t = Σ(x1-x)2
i=1
__________
√ (n-1)
e. none of the above
of 20 observations of an intervally scaled variable which is normally distributed,
but with unknown variance. The correct statistical procedure is
a. z-test.
b. t-test.
c. t-test for difference in two means.
d. analysis of variance.
e. chi-square goodness-of-fit test.
a single population mean
a. assumes the variable is normally distributed
b. applies when the variance of the variable is known
c. applies when the sample size is small; e.g., less than 30
d. is referred to a t-distribution which is completely determined by its degrees
of freedom
e. theoretically applies when the sample is large, e.g., greater than 30, if the
general conditions surrounding its use are satisfied
appropriate for making inferences about a single mean?
a. The variable of interest is normally distributed in the population, σ is known,
and n (number of observations) is large.
b. The variable of interest is normally distributed in the population, σ is known,
and n is small.
c. The variable of interest is normally distributed in the population, σ is
unknown, and n is small.
d. The variable of interest is not normally distributed in the population, σ is
known, and n is large.
e. Calculation of the z-statistic is appropriate in each of these situations.
_ _
population variance (σ) is known (where x is the sample mean, σµ represents the
population mean, and s_ is the standard error of the mean.
x
_
(x - µ)2
a. ______
σ_
x
_
(x - µ)
b. ______
σ_
x
_
(x - µ)2
c. ______
σ
_
(x - µ)
d. ______
σ
_
(x - µ)1/2
e. ______
σ_
x
regarding the equity of two population means it
a. assumes the variable is normally distributed
b. is referred to a t-distribution which is completely determined by its degrees of
freedom and which depends upon the number of observations in each sample
c. assumes the two samples are independent
d. applies when the variance of the variable in each population is known
e. THEORETICALLY applies for all size samples if the general conditions
surrounding its use are satisfied
two observations on the same sample of subjects, and he wishes to investigate if
there is any difference in these two means. The appropriate statistical procedure is
a. z-test for difference in two means
b. analysis of variance
c. paired difference t-test
d. chi-square goodness-of-fit test
e. Kolmogorov-Smirnov test
a. the sample is chi-square distributed and the degrees of freedom is small.
b. the population mean is known.
c. the population variance is unknown.
d. the distribution of the characteristic is normal or the sample is very large such
that the Central-Limit Theorem is operative.
e. both c and d above.
Use the following information to answer the next three questions.
the population mean (µ) is hypothesized to be 200
the sample mean (x) is 220
the sample size (n) is 25
the unbiased sample standard (s) is 15
a. 0.6.
b. 0.9.
c. 1.6.
d. 2.6.
e. 3.0.
a. 4.0.
b. 5.2.
c. 6.7.
d. 7.2.
e. 9.0.
= 05 is 2.064. The 95 percent confidence interval is
a. 204.6 < µ < 230.7.
b. 213.8 < µ < 226.2.
c. 442.1 < µ < 448.6.
d. 511.2 < µ < 514.9.
e. none of the above.
results in
a. larger confidence intervals.
b. significantly more computations on the part of the researcher.
c. no difference in the width of the confidence intervals.
d. smaller confidence intervals.
e. b and c above.
^
(Use the following information for the next three questions.)
A researcher is interested in comparing the usage of bank debit cards by consumers in
rural (r) and urban (u) areas. Each year for the past five years, she has surveyed 500
individuals (one-half urban, one-half rural) randomly selected from across the United
States. She is specifically interested in any differences that may exist between the two
groups with regard to usage. The results of the current study indicate that people in
urban areas use bank debit cards 12 times per month on average (xu), while those in
rural areas use bank cards 10 times per month on average (xr).
comparing the usage rates?
_ _
a. Ho : xu = xr
_ _
b. Ho : xu - xr = µu - µr
c. Ho : µu = µr
d. Ho : µu > µr
_ _
d. HA : xu ≠ xr
calculate the value of the test statistic that would be used in the comparison of the
two means.
a. 0.75
b. 1.33
c. 1.88
d. 1.96
e. none of the above
1.645 at a 90% significance level, which of the following statements are true?
a. The researcher should reject the null hypothesis at the 90% significance level.
b. The researcher might be able to reject the null hypothesis at the 95% level of
significance.
c. The researcher cannot reject the null hypothesis at this significance level.
d. The researcher has provided evidence that people in urban areas use bank
debit cards more than people in rural areas.
e. More information is needed before a decision about the null hypothesis can
be made.
the appropriate test is
a. 0.0029.
b. 0.0527.
c. 0.00128.
d. none of the above.
e. more information is necessary in order to calculate the variance for this
example.
statistic is
a. z=1.64.
b. z=1.96.
c. z=0.74.
d. z=0.93.
e. more information is necessary in order to calculate the z statistic for this
example.
