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 R-squared Adj R-squared 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