( 4 ) Quantitative Analysis

Scenario: As Chief Policy Analyst for Governor Jerry Brown, you are commissioned to conduct a public opinion poll to measure support for the Governor’s education funding proposals, specifically the initiative proposals that will be voted on in the November 2012 statewide election. Your assistant provides you with some tables and summary information about the sample.

The sampling error at the 95 percent confidence interval varies by sub-group and includes weighting conditions: For the 1,310 registered voters, it is ±3.7 percent; for the 823 likely voters, it is ±4.3 percent; for the 620 public school parents, it is ±6.2 percent. Sampling error is only one type of error to which surveys are subject. Results may also be affected by factors such as question wording, question order, and survey timing.

The sample distribution for party identification:

45% Democrat

31% Republican

21% No party preference

3% another party

Table 1: Likely Voter Support for the Governor’s Tax Initiative

"Governor Brown and others have proposed a tax initiative for the November ballot titled the ‘Temporary Taxes to Fund Education. Guaranteed Local Public Safety’ …If the election were held today, would you vote y e s or n o on the proposed tax initiative?" *

*Question was asked of self-identified likely voters only.

(4.1a) What is the probability of a likely voter supporting Gov. Brown’s initiative? How confident can you be about this estimate? Calculate the range of the confidence interval for your estimate using the "sampling error" information: what does it mean, both statistically and substantively? (2)

(4.1b) If you wanted to calculate the probability that likely voter support for the initiative was greater than 50%, which of the following test statistics would you use, and why? (2)

1. t-test
2. z-test
3. Pearson’s R
4. ANOVA

(4.1c) Explain the relationship between sampling error and sample size (2)

Table 2: Likely Voter Support for Various Revenue Generation Mechanisms

(4.2a) The governor wants to know (with 95% confidence) if voters support increasing the state sales tax for education. Here’s the long answer:

n= 823 X= 46% α =.05

p ^{^} ± Z _α/2 * √ ( pq /n ) = .46 ± 1.96 √ ( ((.46)(.54))/823 )

= .46 ± 1.96 √ .2484/823

= .46 ± 1.96 √ .0003

= .46 ± .034

Confidence Interval= (.457, .494)

Explain what statistical test is being done and interpret the steps and substantive results for the Governor. (3)

(4.2b) If you wanted to statistically test for differences in support for tax increases between different party identification groups, what would be the appropriate test statistic and why? (2)

Table 3: Preferences for Improving the Quality of K-12 Education

"To significantly improve the quality of California’s K–12 public schools, which of the following statements do you agree with the most? We need to use existing state funds more wisely, we need to increase the amount of state funding, or we need to use existing state funds more wisely and increase the amount of state funding."

(4.3a) The data in Table 3 suggests that voters are about evenly split between supporting only better use of existing funds, and using some combination of increased funding with better use. If you were asked to estimate a regression model of support for increased funding, based on this question, how would you go about creating and coding your dependent variable? Explain in detail. (3)

(4.3b) Explain how it is possible to take categorical differences between people, like party identification or gender, and turn them into variables that can be used in regression analysis. Explain your answer. (3)

(4.3c) For each of the two data points that have lines drawn in the scatterplot below, identify the line segments that corresponds to the Total Sum of Squares, the line segment that corresponds to the Regression Sum of Squares, and the line segment that corresponds to the Residual Sum of Squares. Please include the labeled graphic in your answer (hand-labeling is okay; make sure each line segment for both data points is clearly labeled). Using non-technical (non-math) language, explain what the terms Total Sum of Squares, Regression Sum of Squares and Residual Sum of Squares mean. (4)

(4.3d) Political scientists want to predict the dependent variable (y) better than the mean. What exactly do we mean by this? Use the diagram to help illustrate your answer. (4)

Y

X

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