Download PLSC 309: Quantitative Political Analysis

PLSC 309: Quantitative Political Analysis
Midterm Exam #2
November 6, 2009
Name______________________________________
True or False (2 points each)
1. _____ A stratified sample is a probability sample in which elements sharing one or more
characteristics are grouped, and elements are selected from each group in proportion to
the group’s representation in the total population.
2. _____ By subtracting the minimum value from the maximum value in a batch of
numbers, you can calculate the absolute deviation.
3. _____ A non-probability sample occurs when each element in the population has a
known probability of inclusion in the sample.
4. _____ On average, a sample statistic will equal the value of a population parameter.
5. _____ Statistical inference involves using what we know to be true about a sample to
deduce what is likely to be true about the population.
Multiple Choice (2 points each)
1. A sample in which respondents are used to identify other persons who might qualify for
inclusion in the sample is called:
a. A snowball sample
b. A systematic sample
c. A cluster sample
d. A simple random sample
2. The incorrect or mistaken rejection of a true null hypothesis is a:
a. Type II error
b. Standard error of the mean
c. Type I error
d. Sample bias
3. The determination of statistical significance for a cross-tabulation requires the calculation
of a statistic called a(n):
a. Gamma
b. Chi-square
c. Analysis of variance
d. F-ratio
4. Which of the following is resistant to outliers?
a. Mean
b. Median
c. Mode
d. Both b and c
5. A statement that a population parameter equals a specific value (e.g. 0) is called a(n):
a. Alternative hypothesis
b. Null hypothesis
c. Empirical claim
d. Sampling distribution
Fill-in-the-Blank (2 points each)
1. A measure of ______________________locates the middle or center of a distribution
and describes a typical case.
2. ___________________ is the number of meaningful peaks in a frequency distribution of
data.
3. A measure of ______________________ describes in a single number or coefficient the
kind and strength of relationship between the values of two variables.
4. ___________________ is a measure of the degree to which a distribution is
asymmetrical.
5. The ___________________ are those outcomes so unlikely to occur if the null is true
that, should one of them appear, you can reject the null.
Word Problems
1. The table below contains life expectancy data for females in 8 European countries.
Calculate the following descriptive statistics. (20 points)
i. Mean
ii. Median
iii. Interquartile range
iv. Standard deviation
v. Trimmed mean (Assume one value from each end of the distribution has
been cut.)
Country
Belgium
France
Germany
Italy
Netherlands
Norway
Portugal
United Kingdom
Life Expectancy: Females
76.8
80.5
78.4
78.6
79.9
75.7
72.4
77.9
2. You want to test the hypothesis that, on average, Americans are ideologically moderate.
You obtain data from the 2004 National Election study. Ideological self-placement is
measured on a seven-point scale on which 4 represents the middle or moderate position.
Consequently, you let the null hypothesis be H0: μ = 4. You then make the alternative
hypothesis HA: μ ≠ 4. You set the level of significance at 0.01. For a sample of N = 25,
the mean ideology score is 4.44 with a standard deviation of 1.23. (20 points)
a. What is the critical value?
b. What is the observed test statistic?
c. Do you reject the null hypothesis or not? Why?
d. What is the importance of this finding for understanding contemporary American
politics?
3. Look at the table below. (18 points)
a. Calculate the following expected frequencies if there were no relationship
between race and opinion about stationing American troops in Iraq.
i. Whites in favor of keeping troops in Iraq
ii. Whites in favor of bringing troops home
iii. Nonwhites in favor of keeping troops in Iraq
iv. Nonwhites in favor of bringing troops home
b. Calculate the appropriate observed test statistic.
c. Calculate the degrees of freedom for the table.
d. Set the level of significance at 0.05. What is the critical value?
e. Do you reject the null hypothesis that there is no relationship between race and
opinion? Why or why not?
4. You want to test that the hypothesis that democracies have a higher average number of
social welfare programs (SWP) than autocracies. Suppose you obtained independent
random samples of N1 = 25 democracies and N2 = 35 autocracies. The sample SWP
mean and variance for democracies are 14.5 and 3.2, respectively. The sample SWP
mean and variance for autocracies are 5.8 and 2.2, respectively. (12 points)
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. What sampling distribution is appropriate for testing these hypotheses?
d. What is the critical value if you want the probability of a Type I error to equal
0.01?
e. Calculate the observed test statistic.
f. Do you reject the null hypothesis? Why or why not?