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Appendix 14
Chi-Square Tests
a. the subjects are matched.
b. frequencies are unimportant.
c. the researcher is interested in all classes of the variable and does not wish to
dichotomize it.
d. the trials are dependent.
e. more than two related samples are being compared.
a. The chi-square distribution is completely determined by the degrees of freedom.
b. The mean of the chi-square distribution is equal to the number of degrees of
freedom.
c. The variance of the chi-square distribution is equal to two times the number of
degrees of freedom.
d. b and c above
e. all of the above
a. expected number of cases in each category is 10 or more.
b. expected number of cases in each category is 5 or more.
c. expected number of cases in each category is 3 or more.
d. actual number of cases in each category is 10 or more.
e. actual number of cases in each category is 5 or more.
(Use the information below for the next two questions.)
A major car manufacturer was interested in whether its midsize car was selling
consistently in two markets with respect to the annual income of the car purchasers.
500 new car buyers in Chicago and Miami were surveyed. In Chicago the following
pattern was observed:
<$20,000 5%
$20,000-$29,999 20%
$30,000-$39,999 40%
$40,000-$49,999 30%
>$50,000 5%
Among those surveyed in Miami, 20 earned under $20,000; 70 earned between
$20,000 and $30,000; 265 earned between $30,000 and $40,000; 125 earned between
$40,000 and $50,000; and 20 earned more than $50,000.
were consistent with Chicago's. The appropriate degrees of freedom for the Chi-
square test would be
a. 4.
b. 5.
c. 500.
d. 499.
e. none of the above.
a. 0.883.
b. 36.3.
c. 11.95.
d. -0.542.
e. not enough information is provided to calculate the value.
For an alpha level of .10 (i.e., alpha = .10) and 4 degrees of freedom, the critical value
of the chi-square statistic is 7.78. The appropriate conclusion is that
a. the sample result is likely to be attributed to chance alone.
b. the null hypothesis should not be rejected.
c. the null hypothesis should be rejected.
d. a and b above are correct.
e. a and c above are correct.
pattern of frequencies is in accord with a stated null hypothesis. The preferred
statistical technique is:
a. the z-test for one mean
b. Chi-square goodness-of-fit test
c. the z-test for two means
d. the Kolmogorov-Smirnov test
e. the z-test for one proportion
(Use the following information for the next three questions.)
A clothing manufacturer traditionally makes sweatshirts from three different fabrics, A, B
and C. Over the years the percentages sold of each fabric are 50, 35, and 15, respectively.
Recently, the manufacturer began producing running suits from the same three fabrics.
During the first three months of production, the company received orders for 6,500 suits
made from fabric A, 3,400 from fabric B, and 2,700 from fabric C.
first three months based on past years' sales results of sweatshirts?
a. 3,500
b. 1,190
c. 4,410
d. 4,500
e. none of the above
are similar to what would be expected given the previous sales history of sweatshirts
made of the three fabrics?
a. Kolmogorov-Smirnov test
b. z-test to compare proportions
c. Chi-square test
d. T-test for two means
e. none of the above
sales (by fabric type) of the new running suit correspond to the expected pattern?
a. 136.21
b. 584.81
c. 0.973
d. 422.13
e. none of the above
the observed number of cases falling in the ith category, Ei is the expected number of
cases falling in the ith category; and k is the number of degrees of freedom.
k
a. Σ [Oi-Ei]2
i=1 _______
Ei
k
b. Σ Oi2-Ei2
i=1 _______
Ei
k
c. Σ Oi-Ei
i=1 _______
Ei2
k
d. Σ Ei-0i
i=1 _______
Ei2
k
e. Σ (Ei-0i/2)
i=1 _______
Ei
a. determining whether two random samples come from populations with the same
median.
b. analyzing observations on the same individual in a pretest-posttest experiment.
c. an analysis that involves two related samples.
d. determining whether a given set of observations has indeed been drawn at random
from a single population.
e. investigating the independence of variables in cross classifications.
a. To generate the expected frequencies for each cell in a chi-square contingency table
test, one need simply multiply the marginal frequencies and divide by the total
number of cases.
b. The marginal total of a row in a chi-square contingency table test is determined as
the product of the expected frequencies for that row.
c. In a contingency table test, the null hypothesis is that the variables of classification
are independent.
d. The expected number of cases in each cell in a contingency table test rest on the
assumption that the variables of classification are independent.
e. When the observations forming the cross tabulation are related as in a before-after
experiment, the chi-square contingency table is not applicable.
of freedom for the chi-square test statistic is
a. 3,3.
b. 15.
c. 3,12.
d. 9.
e. to determine the appropriate degrees of freedom one must know n, the number of
subjects in the experiment.
a. -1,1.
b. 0,1.
c. 0, and an upper limit which is a function of the number of categories for each
variable.
d. -1, and an upper limit which is a function of the number of categories for each
variable.
e. none of the above.
freedom in a two-way contingency table is given by
a. rc.
b. (r + 1)(c + 1).
c. (r - 1)(c - 1).
d. r - 1
c - 1.
e. r + 1
c + 1.
a. The contingency coefficient is directly related to the chi-square test.
b. Its upper value limit is determined by the number of categories in a problem.
c. Some of the difficulties encountered in interpreting the contingency coefficient are
overcome by squaring the coefficient, thereby obtaining the proportion of variance
in the criterion variable explained by the predictor variable.
d. The contingency coefficient as a measure of association is difficult to interpret
purely by examining the calculated value.
e. The contingency coefficient provides a measure of the strength of the association
between the variables.
attributes should use
a. the contingency coefficient.
b. t-test for nominal data.
c. Pearson's product moment correlation coefficient.
d. the coefficient of consistency.
e. none of the above.
a. the chi-square correction for attenuation.
b. the index of predictive association.
c. the chi-square test for distribution symmetry.
d. the contingency coefficient.
e. the coefficient of concordance.
2
2
+
=n
C
(Use the following information for the next six questions.)
Calories Consumed Weight of Adult Male in Pounds
per Day <119 120-199 >200 Total
__________________________________________________________________
<1499 16 20 4 40
1500-2999 4 90 16 110
>3000 0 10 40 50
__________________________________________________________________
Total 20 120 60 200
200 lbs. or more and consume 3000 or more calories per day.
a. 40
b. 15
c. 55
d. 20
e. none of the above
contingency table analysis?
a. Compare the calculated expected frequencies with the observed frequencies using
the t-test.
b. Compute the contingency coefficient.
c. Compute the chi-square
d. Compute the r2
e. None of the above.
a. 9
b. 6
c. 199
d. 198
e. none of the above
number of calories consumed per day by adult males?
a. <1499
b. 1500-2999
c. >3000
d. 2250
e. none of the above
weight of adult males. Calculate the index of predictive association.
a. 0.00
b. 0.44
c. 1.00
d. 0.40
e. none of the above
by taking weight into account?
a. 73%
b. 63%
c. 67%
d. 77%
e. none of the above
FALSE?
a. The index of predictive association is useful when nominally scaled data are
available and when we are interested in the degree of improvement in predictions of
the criterion variable brought about by considering the classes of the predictor
variable.
b. The index of predictive association is equal to one, if the B classification is of no
help in predicting the A classification.
c. The index of predictive association gA.B. measures the relative decrease in the
probability of error by taking account of the B classification in predicting the A
classification over the error of prediction with the B classification unknown.
d. a and b above
e. a and c above
60%. N.M = .5. If the M classification is taken into account, of the N classification
should now be predicted correctly.
a. 30%
b. 40%
c. 50%
d. 60%
e. 70%
Suppose the following table resulted from a cross-classification analysis of variables X
and Y.
_____________________________________________________
X1 X2 X3 X4 Total
_____________________________________________________
Y1 10 0 0 0 10
Y2 0 20 0 0 20
Y3 0 0 30 0 30
Y4 0 0 0 70 70
_____________________________________________________
TOTAL 10 20 30 70 130
a. is 0.
b. is .5.
c. is -1.
d. is 1.
e. cannot be determined.
Suppose the following table resulted from a cross-tabulation analysis of variables X,
family income, and Y, years of education
_____________________________________________________
Years of
Education 0-5000 5,001-10,000 10,000 or more Total
_____________________________________________________
0 to 8 20 6 3 29
9 to 12 15 8 10 33
13 or more 4 4 30 38
_____________________________________________________
TOTAL 39 18 43 100
______________________________________________________
when predicting the A classification from the B classification, the index of predictive association for
the above data is
a. 0.
b. .25.
c. .32.
d. .50.
e. .67.
a. t-test
b. linear regression model
c. cross-tab
d. chi-square
e. contingency index
the consumer bought your brand, 0 if they bought some competitor brand. Which of the
following uses of this variable is improper:
a. a t-test on a preference rating scale, using “brand” to define the groups
b. a regression using age, household size, and income to predict “brand”
c. a regression using “brand” to predict preference
d. a log linear model applied to a “brand” by gender cross-tab
e. a logit using age and income to predict “brand”
m
m
bbm
BA nn
nn
.
.
.. −
−
=
