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(solution) Hello there! I'm having difficulty completing my statistics
Hello there! I'm having difficulty completing my statistics problem set for my political science course. I completed problems 1 & 2 relatively easily, but I'm struggling with the rest of the assignment. Help please?
Name:_______________________________ GSI:________________________________ Political Science 3 Homework # 4 Note: It is highly recommended that you show your work. This means setting up the problem
by writing out the equation(s) being used (if an equation is involved) and showing that you
know what to plug into the equation(s). Partial credit may be given for incorrect answers if the
work shows that you made a simple error. On the questions that specifically ask you to show
your work, full credit will not be given without it.
1. A recent poll asked people whether they supported passing a constitutional
amendment to ban burning of the national flag using a 1 to 100 scale.?1? means that
they do not support passing the amendment at all and ?100? means they support it
completely. The sample was random (from the population of US adults) and included
886 people, 350 of whom were women, and 536 of whom were men. The mean score for
women was 82.6, while the mean score for men was 78.4.
a) [4 points] Is the difference in means statistically significant at the 5% level? Assume
the standard deviation for both men and women is 3.5. Show your work.
b) [4 points] If the standard deviation for men is 1.4 and the standard deviation for
women is 1.2, is the difference in means statistically significant at the 5% level?
Show your work. 2. The following table is based on a sample of high school seniors and their parents. The
data comes from a study conducted by Jennings and Niemi, in which they explore the
party identification of parents and their children. a) [2 points] What is the percentage of students who share the same party identification
as their parents? 1 b) [3 points] What is the relationship between students? party identification and the
party identification of their parents? (In other words, do students generally follow
their parents? party identification, or not?)
c) [4 points] Based on these data, can we say if the relationship is causal? Explain your
answer.
d) [6 points] Suppose you were exploring the hypothesis that there is a relationship
between parents? and children?s party identification. Would we be correct in
inferring that such a relationship also exists in the population? Explain your answer.
What is the probability that any relationship we found is due to pure chance? 3. Tens of thousands of people die each year on America?s highways. How can the
number of fatalities be reduced? In the next few questions, we explore trends in traffic
fatalities across the 50 states and potential solutions to the problem. Consider the table
below, indicating summary statistics of the number of traffic deaths per million miles
driven across all 50 states, in 1985 and 1992.
Variable 
Obs
Mean
Std. Dev.
Min
Max
+traffic_1985 
50
2.294
.6079104
1.9
4.4
traffic_1992 
50
1.744
.449108
1
2.7 a) [2 points] What is the average change across states between 1985 and 1992 in
traffic deaths per million miles driven?
b) [4 points] Assume that these observations represent a random sample of all
years. How likely would we get the average change found in part (a) if the true
difference in the population were actually zero? Show your work.
c) [4 points] Can we reasonably claim that there is a difference in traffic fatalities
between 1985 and 1992? Explain your reasoning. 4. Continuing with your study of traffic fatalities, you have been charged with figuring
out what policy would best curb the death rate. You discover that states have tried a
number of solutions in the past, including raising the drinking age to 21, mandating the
use of seat belts and helmets, and setting a maximum speed limit of 65 miles per hour.
These various initiatives make you wonder whether states that pass one of these
measures are also more likely to pass another. You therefore construct the table on the
following page, which indicates how many states have passed mandatory seat belt laws
and/or have imposed a 65 mile per hour speed cap. 2  Mandatory seatbelt law
65 MPH 
Cap

no
yes 
Total
++no 
0
8 
8
yes 
8
24 
32
++Total 
8
32 
40 a) [2 points] What percentage of states has passed both seat belt laws and a speed limit
law? Show your work.
b) [2 points] Of the states that have imposed a 65 MPH speed cap, what percentage
does not mandate seat belts? Show your work.
c) [4 points] Test the claim that states which pass mandatory seat belt laws tend also to
impose 65 MPH speed limits. Is there a relationship? Why or why not?
5. [5 points] You hate the laws imposing 65 MPH speed limits, but are nonetheless curious
as to whether the law actually reduces highway deaths. Using information in the table
below, perform an appropriate test to determine whether speed limits reduce traffic
deaths or not. Explain your reasoning.
> There IS a speed limit law.
Variable 
Obs
Mean
Std. Dev.
Min
Max
+traffic_1992 
8
1.5
.3338092
1.1
2.1
> There IS NOT a speed limit law.
Variable 
Obs
Mean
Std. Dev.
Min
Max
+traffic_1992 
32
1.909524
.4410683
1
2.7 6. How much student improvement takes place in PS3? One way to examine this question is to look at exam performance over time. On the following page is a scatterplot relating exam scores on the first two midterms, with a line of best fit drawn through the points. Each point represents a student in the class. 3 1
.9
.8
Midterm 2 Score
.4 .5 .6 .7
.3
.2
.1
0
0 .1 .2 .3 .4
.5
.6
Midterm 1 Score .7 .8 .9 1 a) [2 points] Describe in a few sentences what this trend implies about the association between scores on the first midterm and scores on the second midterm. b) [4 points] To what extent does this graph indicate an improvement in scores between the two midterms? Explain how you arrived at your answer. 7. The table below shows the results of a bivariate regression of midterm 2 scores on midterm 1 scores (using point totals rather than fractions, and performed in Stata, a popular statistics package). Source 
SS
df
MS
+Model  14335.1038
1 14335.1038
Residual  22680.6453
280 81.0023045
+Total  37015.7491
281 131.728645 Number of obs
F( 1,
280)
Prob > F
Rsquared
Adj Rsquared
Root MSE =
=
=
=
=
= 282
176.97
0.0000
0.3873
0.3851
9.0001 mid2 
Coef.
Std. Err.
t
P>t
[95% Conf. Interval]
+mid1 
.6251181
.0469905
13.30
0.000
.5326186
.7176177
_cons 
24.45228
2.639302
9.26
0.000
19.25689
29.64767 4 a) [3 points] Is the relationship between scores on midterm 1 and midterm 2 statistically significant at the .05 level? Why or why not? What sampling assumptions have to be made to conclude this? b) [5 points] Using the information in the table, compute a 99% confidence interval for midterm 1 (mid1). Is the relationship between scores on midterm 1 and midterm 2 statistically significant at the .01 level? Why or why not? c) [5 points] Suppose a student got 50 points on midterm 1. What would the expected performance of that student be according to this bivariate model? Explain how you arrived at your answer. 5
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