# Test 2: Part B- SOCI 3443 Social Statistics | Complete Solution

Test 2: Part B- SOCI 3443 Social Statistics
CH6 to CH9
Please well prepared this exam using class material to answer these questions and you also have to take
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This exam will be due by 11:59 CST Sunday, March 27th.

Name _______________________________________________

1

Problem set 1: Use the following information to answer questions 1-3 (10 points):
A criminologist developed a test to measure recidivism, where low scores indicated a lower probability
of repeating the undesirable behavior. The test is normed so that it has a mean of 140 and a standard
deviation of 40.
1. What is the percentile rank of a score of 182 (4 pts)?

2.

What percentage of scores falls between 60 and 180 (4 pts)?

3. Suppose an individual is in the 79.10th percentile in this test, what is his or her corresponding
recidivism score (2 pts)?

2

Problem set 2: use the following information to answer questions 4-7 (10 points total):
An upper-level sociology class at a large urban university has 120 students, including 22 seniors, 68
juniors, 12 sophomores, and 18 freshmen.

4. Imagine that you choose one random student from the classroom (perhaps by using a
random number table). What is the probability that the student will be a junior (2 pts)?

5. What is the probability that the student will be a freshman (2 pts)?

6. If you are asked to select a proportionate stratified sample of size 30 from the classroom,
stratified by class level (senior, junior, etc.), how many students from each group will
there be in the sample (4 pts)?

7. If instead you are to select a disproportionate sample of size 28 from the classroom, with
equal numbers of students from each class level in the sample, how many freshmen will
there be in the sample (2 pts)?

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Problem set 3: use the following information to answer questions 8-12 (10 points total):
The 2006 General Social Survey contains information on the number of hours worked by a
respondent each week. The mean number of hours worked per week is 39.07, with a standard
deviation of 12.51. The sample size is 121.
8. Estimate the value of the standard error (2 pts).

9. Calculate a 95 percent confidence interval for these data (2 pts).

10. Provide a one or two sentence interpretation of this result (2 pts).

11. Using this data, provide a hypothetical numerical example which demonstrates that the
precision of a confidence interval is in part a function of sample size (2 pts).

12. Using this data, provide a hypothetical numerical example which demonstrates that the
precision of a confidence interval is a function of both sample size and the level of
confidence (2 pts)?

4

Problem set 4: use the following information to answer questions 13-14 (5 points total):
The GSS 2010 measures the amount of hours individuals spend on the Internet per week. Men
use the Internet 10.17 hours per week (standard deviation = 11.71, N = 118), while women use
the Internet 9.08 hours per week (standard deviation = 12.26, N = 157).
13. Test the research hypothesis that men use the Internet more hours than women, set alpha
at .05 (4 pts)?

14. Would your decision have been different if alpha were set at .01 (1 pt)?

5

Problem set 5: use the following information to answer questions 15-17 (5 points total):
Suppose you are interested in comparing the mean number of hours worked by sex.
Weekly Hours Worked Women
Range

59

Minimum value

11

Maximum value

70

Mean
Variance

37.28
142.88

Standard deviation

11.95

Sum

2013

Number of observations

54

Weekly Hours Worked Men
Range

60

Minimum value

5

Maximum value

65

Mean
Variance

42.31
100.00

Standard deviation

10.00

Sum

1,227

Number of observations

29

15. Use all or some of the information above to calculate the value of the independent
samples t- statistic (3 pts).

16. Suppose you are interested in comparing the mean number of hours worked by sex.
Using the information above, calculate the number of degrees of freedom associated with
an independent samples t-statistic (2 pts).

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17. Define Type I and Type II error (Extra 4 pts).

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