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

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)?
    

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)?

 
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)?

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)?

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    37.28
    Variance    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    42.31
    Variance    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).

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