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Exam 2 Practice Test
This practice exam is based on a test from a previous semester. You are not responsible for material covered in
questions 22, 26 or 29. The exam will also have an essay question.
Multiple Choice
Identify the choice that best completes the statement or answers the question. (1.5 Pts each)
____
____
____
____
____
____
____
____
1. If a Z score is 0 then the value of the corresponding raw score would be
a. 0
b. the same as the mean of the empirical distribution
c. the same as the standard deviation of the empirical distribution
d. probably a negative number
2. A defining characteristic of the normal curve is that it is
a. theoretical
b. positively skewed
c. negatively skewed
d. perfectly skewed
3. The area beyond  2 standard deviations contains approximately what % of the area under the normal curve?
a. 75%
b. 50%
c. 9%
d. 5%
4. The Z score table gives the area between a score and the mean. For a Z score of 1.00 that area (in
percentages) is
a. 34.13%
b. 34.13%
c. 68.26%
d. 68.26%
5. Column C in the normal curve table lists "areas beyond Z". This is the area
a. below a positive Z score
b. above a negative Z score
c. between two positive Z scores
d. above a positive Z score
6. The area between the mean and a Z score of +1.50 is 43.32%. This score is less than ____ of the scores in the
distribution.
a. 43.32%
b. 6.68%
c. 3.32%
d. 93.32%
7. The mean score on a final chemistry exam was 75, and the standard deviation of the scores was 5. If the
distribution is normal and your score was 70, what percentage of the scores was lower than yours?
a. 15.87%
b. 30.00%
c. 34.13%
d. 50.00%
8. The probability that a randomly selected case will have a score beyond ± 1.00 standard deviation of the mean
is
____
9.
____ 10.
____ 11.
____ 12.
____ 13.
____ 14.
____ 15.
____ 16.
____ 17.
a. .6826
b. .5000
c. .3174
d. 1/2 of the area of 1 standard deviation
Statistics are to parameters as
a. samples are to populations
b. populations are to samples
c. medians are to standard deviations
d. percentages are to proportions
Social scientists use inferential statistics to generalize to populations after they have
a. collected a representative sample
b. collected all the information possible from the entire population
c. collected an EPSEM sample from the population of interest
d. collected at least 100 cases from all possible populations
The fundamental principle of probability sampling is that a sample selected by ____ is very likely to be ____.
a. EPSEM, representative
b. stratification, large
c. telephone polls, cheap
d. clusters, stratified
Unlike the sample and population distributions, the sampling distribution is
a. empirical
b. theoretical
c. random
d. EPSEM
The standard error of the mean is the same thing as
a. the standard deviation of a sample
b. the standard deviation of a population
c. the standard deviation of a sampling distribution
d. the variance of a sample
When we use larger samples (N > 100) we can assume a normal sampling distribution because of
a. common sense
b. the Central Limit Theorem
c. what we know about the population
d. what we know about the sample
In estimation procedures, as the alpha level decreases, the corresponding Z scores
a. move closer to the mean of the sampling distribution
b. move away from the mean of the sampling distribution
c. become negative
d. become positive
Which sample size will produce the confidence interval with the smallest width?
a. 100
b. 200
c. 500
d. 1000
The central problem in the case of one sample hypothesis test is to determine
a. if a sample is random
b. if sample statistics are the same as those of the sampling distribution
c. if parameters are representative of population
d. if a sample came from a population with a certain characteristic
____ 18. The null hypothesis in the one sample case is a statement of
a. agreement with the research hypothesis
b. rejection
c. acceptance
d. no difference
____ 19. In tests of significance, if the test statistic falls in the critical region, we may conclude that
a. the population distribution is normal
b. the null hypothesis can be rejected
c. the research hypothesis is true
d. our sample size was too small
____ 20. If the critical region begins at Z(critical) =  2.56 and the test statistic is  2.50, we
a. fail to reject the null hypothesis
b. reject the null hypothesis
c. cannot make a decision because the test statistic is so close to the critical region
d. change the alpha level
____ 21. A sample of people attending a professional football game averages 13.7 years of formal education while the
surrounding community averages 12.1. The difference is significant at the .05 level. What could we conclude?
a. the null hypothesis should be accepted
b. the research hypothesis should be rejected
c. the sample is significantly more educated than the community as a whole
d. the alpha level is too low
____ 22. In a one-tailed test of hypothesis, the entire ____ should be placed in either the upper or lower tail of the ____
a. critical area, sampling distribution
b. sample mean, population distribution
c. Z score, critical area
d. sampling distribution, sample distribution
____ 23. When we decide on a value for alpha, we are
a. defining the likelihood of accepting the alternative hypothesis
b. establishing whether the test will be one or two tailed
c. setting the probability of committing a Type I error
d. setting the probability of a one-tailed test
____ 24. When testing for the significance of the difference between a sample mean and a population mean, degrees of
freedom are equal to
a. N  1
b. N + 1
c. alpha
d. 1  alpha
____ 25. When random samples are drawn so that the selection of a case for one sample has no effect on the selection
of cases for another sample, the samples are
a. dependent
b. independent
c. simple
d. systematic
____ 26. When conducting hypothesis tests for two sample means, the term 1  2 in the numerator of the formula
reduces to zero because
a. the standard deviations are calculated first
b. the tests are conducted at very low alpha levels
c. the samples are independent as well as random
d. the null hypothesis is assumed to be true
____ 27. When testing for the significance of the difference between two sample means, we must first estimate ____
before we can compute the test statistic.
a. the standard deviation of the sampling distribution
b. the standard deviations of the samples
c. the population means
d. the critical region
____ 28. For all tests of hypothesis, the probability of rejecting the null is a function of
a. the size of the observed differences
b. the alpha level and the use of one- or two-tailed tests
c. sample size
d. all of the above
____ 29. Four test of significance were conducted on the same set of results:
For test 1: alpha = 0.05, two-tailed test.
For test 2: alpha = 0.10, one-tailed test.
For test 3: alpha = 0.01, two-tailed test.
For test 4: alpha = 0.01, one-tailed test.
____ 30.
____ 31.
____ 32.
____ 33.
____ 34.
Which test is most likely to result in a rejection of the null hypothesis?
a. Test 1
b. Test 2
c. Test 3
d. Test 4
The larger the sample size, the
a. more important the observed difference
b. more likely we are to reject the null hypothesis
c. less likely we are to reject the null hypothesis
d. lower the Z score
Random samples of 1546 men and 1678 women have been given a scale that measures support of legal
abortion. Men average 12.45 and women average 12.46 and the difference is significant at the 0.05 level.
What can we conclude?
a. There is an important difference between men and women on this issue.
b. Because of the large sample sizes, these results may be statistically significant but trivial.
c. The difference should be re-tested with a one-tailed test
d. The difference should be re-tested at a higher alpha level
The ANOVA test is designed for dependent variables that have been measured at
a. the interval-ratio level
b. the nominal level
c. the ordinal level
d. any level of measurement
ANOVA is appropriate for situations in which
a. only nominal level variables are involved
b. we are comparing more than two samples or groups
c. the independent variable is interval-ration in level of measurement
d. there are fewer than two samples
A researcher is comparing random samples of white, black, and Hispanic Americans for differences in
income, family size, and years of education. Which of the following tests of significance would be appropriate
for these situations?
a. t test for small samples
____ 35.
____ 36.
____ 37.
____ 38.
b. t test for difference in means
c. ANOVA
d. the test for the significance of the difference between sample proportions
If we reject the null hypothesis in a test using analysis of variance, we are concluding that
a. the populations from which our samples come are different
b. the variable are independent
c. the population variances are the same
d. the sample means are significantly different
The F ratio is equal to
a. SST  SSB
b. the "mean square between" divided by the "mean square within"
c. the "mean square within" minus the "mean square between"
d. the total variance divided by the mean square between
The sampling distribution for the ANOVA test is
a. the Z distribution
b. the t distribution
c. the F distribution
d. None of the above
One limitation of the ANOVA test (and all tests of significance) is that
a. results based on large samples are not reliable
b. both independent and dependent variables must be at least ordinal in level of measurement
c. the population variance is extremely unstable and computations may not be accurate
d. statistical significance is not the same thing as importance in any other sense
Calculations
39) A scale measuring prejudice has been administered to a large sample of respondents. The distribution of scores is
approximately normal, with a mean of 31 and a standard deviation of 5. What percentage of the sample had scores above
35?
40) A scale measuring prejudice has been administered to a sample of 100 respondents. The distribution of scores is from
a population which is approximately normal, with a mean of 31 and a standard deviation of 5. What is the probability the
sample will have a mean less than 30?
42) A researcher has gathered information from a random sample of 178 households. In the sample, there were an average
of 2.1 television sets per household with a standard deviation of s=1.0 . give a 95% confidence interval for the number of
television sets per household in the population.
Short Answer
For each set of SPSS output, answer the following questions.
1) What is the null hypothesis being tested?
2) What is the alternative hypothesis?
3) What type of test is being conducted, single mean test, independent mean test or ANOVA?
4) Should you reject the null hypothesis?
5) Interpret the test results
6) For single mean tests and independent mean tests only, what does the confident interval represent?
7) For single mean tests and independent mean tests only, is the test one-tailed or 2 tailed at a 95% level of confidence?
8) For ANOVA tests only, which means show significant differences?
SPSS Output Set #1
One-Sample Statistics
N
Ideal Number of Children
Mean
2.76
965
Std. Error
Mean
.051
Std. Deviation
1.571
One-Sample Test
Test Value = 3
Ideal Number of Children
t
-4. 755
df
964
95% Confidenc e
Int erval of t he
Difference
Lower
Upper
-.34
-.14
Mean
Difference
-.240
Sig. (2-tailed)
.000
SPSS Output Set #2
Group Statistics
Number of Brothers
and Sis ters
Respondent's Sex
Male
Female
N
641
854
Mean
3.71
3.71
Std. Deviation
2.915
3.031
Std. Error
Mean
.115
.104
Independent Samples Test
Levene's Test for
Equality of Variances
F
Number of Brothers
and Sis ters
Equal variances
as sumed
Equal variances
not ass umed
.335
Sig.
.563
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
90% Confidence
Interval of the
Difference
Lower
Upper
-.009
1493
.993
-.001
.156
-.258
.255
-.009
1405.679
.993
-.001
.155
-.256
.254
SPSS Output Set #3
ANOVA
Age of Res pondent
Sum of
Squares
Between Groups 24697. 368
W ithin Groups
428268.7
Total
452966.1
df
4
1486
1490
Mean Square
6174.342
288.202
F
21.424
Sig.
.000
Post Hoc Tests
Multiple Comparisons
Dependent Variable: Age of Respondent
Bonferroni
(I) RS Highest Degree
Less than HS
High s chool
Junior college
Bachelor
Graduate
(J) RS Highest Degree
High s chool
Junior college
Bachelor
Graduate
Less than HS
Junior college
Bachelor
Graduate
Less than HS
High s chool
Bachelor
Graduate
Less than HS
High s chool
Junior college
Graduate
Less than HS
High s chool
Junior college
Bachelor
Mean
Difference
(I-J)
9.500*
12.390*
11.834*
8.830*
-9.500*
2.891
2.334
-.670
-12.390*
-2.891
-.557
-3.561
-11.834*
-2.334
.557
-3.004
-8.830*
.670
3.561
3.004
*. The mean difference is s ignificant at the .05 level.
Std. Error
1.186
2.059
1.510
1.900
1.186
1.890
1.270
1.716
2.059
1.890
2.108
2.403
1.510
1.270
2.108
1.953
1.900
1.716
2.403
1.953
Sig.
.000
.000
.000
.000
.000
1.000
.662
1.000
.000
1.000
1.000
1.000
.000
.662
1.000
1.000
.000
1.000
1.000
1.000
95% Confidence Interval
Lower Bound Upper Bound
6.17
12.83
6.60
18.18
7.59
16.08
3.49
14.17
-12.83
-6.17
-2.42
8.20
-1.24
5.90
-5.49
4.15
-18.18
-6.60
-8.20
2.42
-6.48
5.37
-10.32
3.20
-16.08
-7.59
-5.90
1.24
-5.37
6.48
-8.50
2.49
-14.17
-3.49
-4.15
5.49
-3.20
10.32
-2.49
8.50
Exam 2 Fall Practice Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
ANS: B
PTS: 1
ANS: A
PTS: 1
ANS: D
PTS: 1
ANS: A
PTS: 1
ANS: D
PTS: 1
ANS: B
PTS: 1
ANS: A
PTS: 1
ANS: C
PTS: 1
ANS: A
PTS: 1
ANS: C
PTS: 1
ANS: A
PTS: 1
ANS: B
PTS: 1
ANS: C
PTS: 1
ANS: B
PTS: 1
ANS: B
PTS: 1
ANS: D
PTS: 1
ANS: D
PTS: 1
ANS: D
PTS: 1
ANS: B
PTS: 1
ANS: A
PTS: 1
ANS: C
PTS: 1
ANS: A
PTS: 1
ANS: C
PTS: 1
ANS: A
PTS: 1
ANS: B
PTS: 1
ANS: D
PTS: 1
ANS: A
PTS: 1
ANS: D
PTS: 1
ANS: B
PTS: 1
ANS: B
PTS: 1
ANS: B
PTS: 1
ANS: A
PTS: 1
ANS: B
PTS: 1
ANS: C
PTS: 1
ANS: A
PTS: 1
ANS: B
PTS: 1
ANS: C
PTS: 1
ANS: D
PTS: 1
21.29%
2.33%
95% confident the mean number of television sets in an American household is between 1.95 and 2.25.