 Answers to Sample Questions for 2/3 Exam
from Previous Years


 Which test statistic  (1) zscore, (2) tscore,
(3) F ratio  would be most suitable for testing
relationships between
 these pairs of variables?

 1.___2___ Difference in mens'
and womens' attendance rates at religious services
 (The ttest, which produces a tscore, is
for difference between means of two nominal
groups. No Ns are mentioned so ttest is
appropriate.)
Return

 2.___1___ Difference in the predicted mean
Republican vote in 1998 by the Gallup poll with 900
interviews and the CBS poll with 1,200.
 (One could also use a ttest, but the
samplesizes are so large that the test statistic
would distribute normally, so a zscore is
appropriate.)
Return
 3.___3___ Literacy rates by countries and a
classification of countries by region.
 (Literacy rates are measured on a
continuous scale, and region is a nominal
variable. So ANOVA is appropriate, and it
produces an F ratio.)
Return
 4. The formula provides
an unbiased estimate of the population:
 1 standard deviation
 (Dividing by N1 corrects for degrees of
freedom.)
Return
 5. The standard error of
the mean is
 3 the standard deviation of the sampling
distribution of means
 (Remember that a standard error of any
statistic is, by definition, the standard deviation
of a distribution of an infinite number of samples
drawn to compute that statistic.)
Return
 6. The standard error of
the mean is equal to

(In this expression, the numerator and
denominator have been squared.)
Return
 7. Given a sample size of 100,
mean of 36, population standard deviation of 5, and
confidence level of .95, the confidence interval for the
mean of the population is closest to
 4 35 to 37
 (This requires applying the formula for
the standard error of the mean: .
So the standard error is .5. You don't simply
add and subtract .5 from your sample mean of 36,
for that would mark off only
one standard error above
and below the mean. The rule of thumb for the
95% confidence interval is to
double the standard error
and then add and subtract it from your
estimate.)
Return
 8. In practical terms, the amount
of accuracy in predicting from national samples to the
U.S. Population is least dependent on
 1 the proportion that the sample is of the
population
 2 The "absolute number of cases in the sample"
is N, and is critical to sample accuracy.
 3 "The population variance for the attribute
being estimated," is used in the numerator of the
formula for the standard error.
 4 "The procedure used in drawing the sample,"
is essential, as each case must have a known
probability of being selected. The % the sample is of
the population gets to be important only when the
sample grows to about 20% of the population, which
rarely occurs in social science research.)
 9. Which of the following terms
does not belong with the other terms?
 4 zscore
 ("Type I error," "alpha level," and "region
of rejection" all pertain to the risk of rejecting
a true null hypothesis.)
Return
 10. Which of the following
statistical distributions is interpreted with reference
to two different degrees of freedom?
 1 F
 (Tables of the t distribution are entered
using only one value for degrees of freedom.
Degrees of freedom are irrelevant to a "skewed"
distribution. A normal distribution is not
dependent on degrees of freedom.)
Return

 11. If one has a directional
hypothesis, he or she especially wants to
 1 make a onetailed test
 (A one tailed test allows for rejecting the
null with a smaller critical value, which means
observing a smaller difference than required with a
two tailed test.)
Return
 12. The sampling distribution of
the difference between two means for independent samples

 4 tends to become normal as the sample sizes
increase.
 (This is the gist of the Central Limit
Theorem.)
Return
 13. In the analysis of variance
model, the null hypothesis of no difference among the
means for the subgroups will tend to be rejected as
 1 the "between group" variance exceeds the
"within group" variance.
 (The null hypothesis asserts that the groups
could be drawn from the same parent population.
This implies that they have similar means and
similar variances. To the extent that differences
"between" groups increases, the groups groups tend
to be different from each other.)
Return
 14. Which statement is true
about data expressed in proportions?
 3 Proportions computed for a dichotomized
variable are simply a type of mean.
 (Suppose you coded a dichotomy, such as sex,
Male=0 and Female=1. Suppose further that you have
a group of 10 people, 4 of whom are males. The mean
for "sex" would be .6, and the proportion would be
.6.)
Return
 15. Another name for "between
groups" sum of squares in the analysis of variance is
 3 explained variation
 (Between groups sum of squares is calculated
on the difference between the group means on a
dependent variable and the grand mean. Big
differences indicate that the groupings of cases
has a strong effect on the values of the dependent
variable.)
Return
 16. An unbiased estimator of a
population parameter is
 1 a statistic whose mean value of its own
sampling distribution is equal to the population
parameter.
 (Thus, the mean (average) value of the
sampling distribution of the statistic being
estimated is equal to the mean (average) value
in the population.)
Return
 17. Calculate the variance for
this set of numbers: 5,5,5,5,5,5
Case

X

mean of X

(x  mean)

(x  mean)^{2}

1

5

0

5

25

2

5

0

5

25

3

5

0

5

25

4

5

0

5

25

5

5

0

5

25

6

5

0

5

25




·(xmean)^{2}=

150

 Variance = 150 / 6
=__25___
Return
 18. According to the table of
areas under the normal curve, what positive and negative
zscore value would be used to establish the region of
rejection for a TWOtailed test nearest to the .04 level
of significance?
 zscore = ___2.05______
 (A zscore of 2.05 marks 0.0202 in one tail. So a
twotailed test would encompass 0.0404 in both
tails.)
Return
 Here is TTEST output comparing Democrat and
Republican Members of Congress, with the dependent
variable being a scale of increasing "conservatism" in
voting on social issues. Answer questions 19 and 20.
VARIABLE NUMBER STANDARD STANDARD
OF CASES MEAN DEVIATION ERROR
DEMOCRATS 248 30.5806 23.441 1.488
REPUBLICANS 180 65.7278 16.318 1.216
Mean Difference = 35.1472
Levene's Test for Equality of Variances:F= 2.06 P= .000
Variances tvalue df 2TailSig
Equal 17.30 426 .000
Unequal 18.28 425.31 .000


 19.Which expression below was used to
compute the degrees of freedom for Equal Variance
estimate of the TTest above?
 4 (N1 + N2  2)
 (Check it out. df = 248 + 180  2 =
426)
Return
 20. Which statement about the
above TTEST output is true? Return
 3 The Fvalue is significant at the .05 level,
indicating that the population variance are equal and
that you are advised to use the Unequal variance
estimate rather than the Equal estimate in checking
the significance of t.


 Below is SPSSx output from MEANS for GNP PER CAPITA
in the POLITY data analyzed by type of government. Answer
questions 21, 22, 23, and 24 with reference to this
output.

DEPENDENT VARIABLE GNPPCA80 GNP PER CAPITA IN US DOLLARS1980
INDEPENDENT VARIABLE POLTYPE TYPE OF POLITICAL SYSTEM
VARIABLE VALUE LABEL MEAN STD DEV CASES
FOR ENTIRE POPULATION 3633.0864 4267.0914 81
POLTYPE 1.00 PARLIAMENT/DEMOCRACY 6511.4815 4608.2098 27
POLTYPE 2.00 DEMOCRATIC & FEDERAL 9598.0000 5869.8825 5
POLTYPE 3.00 MULTIPARTY DEMOCRACY 1322.8571 1334.9746 7
POLTYPE 4.00 DEMOCRATIC FORM 2210.0000 113.1371 2
POLTYPE 5.00 MILITARY GOVERNMENT 895.8333 900.6408 12
POLTYPE 8.00 ONEPARTY COMMUNIST 3587.5000 2431.3180 8
POLTYPE 9.00 ONEPARTY SOCIALIST 2270.0000 494.9747 2
POLTYPE 10.00 ONEPARTY MARXIST 276.6667 140.1190 3
POLTYPE 11.00 ONEPARTY STATE 798.6667 1015.8168 15
SUM OF MEAN
SOURCE SQUARES D.F. SQUARE F SIG.
BETWEEN GROUPS 690959683.13 8 86369960.391 8.1217 .0000
WITHIN GROUPS 765685845.26 72 10634525.629


 21. Showing the math, compute
the MEAN SQUARE for BETWEEN GROUPS to one decimal:
_____________
 Between groups mean square = 690959683.13 / 8 =
86369960.391
Return

 22. Showing the math, compute
the F ratio to one decimal: _____________

 F = 86369960.391 / 10634525.629 =
8.1217
Return

 23. Which statement gives the
most accurate assessment of that relationship?
 3 The null hypothesis can be rejected at the
.01 level.
Return
 24. Under the null hypothesis,
the expected value of Pearson's r is
 4 zero
 (That is, the null hypothesis asserts that
the two variables are not correlated. So any
correlation you observe, may have observed by
chance.)
Return
 25. What condition exists when
the variance of Y remains the same for different values
of X?
 1 homoscedasticity
Return
 26. This formula for testing the
significance of r:
, assumes that
4 the test is against the null
hypothesis that the population correlation, r (rho),
is equal to 0. Return

 27. If
data for 2 variables are transformed into zscores and
then correlated,
[This topic was not
covered.]
 1 the product moment
correlation will be equal to the beta coefficient
in the associated regression
equation.
 2 the beta coefficient will
be equal to the bcoefficient in the regression
equation.
 3 the intercept in the
regression equation will be equal to 0.
 4 all of the above are
true.
Return
 28.Tested against the null
hypothesis, a highly significant correlation merely
indicates that
 1 it is unlikely that there is no relationship
between the variables in the universe.
Return

 29. Which statistic is most
appropriate for testing the significance of the
difference among means for four independent samples?
 3 F ratio
Return
 30. The condition of
heteroscedasticity is best shown in which diagram?

 1 This one
 (By convention, the base line represents the
Xvariable and the perpendicular line the
Yvariable. Q. 25 above defines "homoscedasticity."
Heteroscedasticity obtains when the variance of Y
is not constant for different values of
X.)
Return
