answers to practice final exam

1 Simon Fraser University Department of Political Science FALL 2014 QUANTITATIVE METHODS IN POLITICAL SCIENCE Final Exam Time allowed TWO Hours Candidates must NOT write anything until the start of the examination period is announced Answer ALL questions on this examination sheet For full marks show all work Numbers in square brackets at the end of each question indicate the number of marks available for the question. Total Marks: 100 + 10 bonus points No electronic devices capable of storing and retrieving text, including electronic dictionaries, may be used. Calculators are permitted but graphing calculators are not. DO NOT open examination paper until instructed to do so

2 1. There are four hurdles we need to overcome in order to demonstrate a causal relationship between ? and ? . Which hurdle might we use bivariate hypothesis testing to overcome? [2] Is there covariation between X and Y? ( Half points for “the third” ) 2. List the three parts of a research design: [3] i) hypothesis/hypotheses ii) method of data collection iii) method of analysis 3. In a recent survey of 1000 randomly sampled British adults 18 years and older, 56% of respondents supported the nationalisation of utilities such as gas and electricity. Calculate a 95% confidence interval for the proportion of British adults supporting the nationalization of utilities. [5] 𝑠𝑒 = √ 𝑃(1−𝑃) 𝑁 = √ 0.56×0.44 1000 = 0.0157 95%𝐶𝐼 = 𝑃 ± 1.96 × 𝑠𝑒 95%𝐶𝐼 = 0.56 ± 1.96 × 0.0157 95%𝐶𝐼 = 0.56 ± 0.0308 (0.529, 0.591) 95%𝐶𝐼 = 𝑃 ± 2 × 𝑠𝑒 95%𝐶𝐼 = 0.56 ± 2 × 0.0157 95%𝐶𝐼 = 0.56 ± 0.0314 (0.529, 0.591) 4. You run a regression and the total sum of squares (TSS) is reported as 20 and the residual sum of squares (RSS) is reported as 10. Calculate the R -squared value: [4] ? 2 = ??? − ??? ??? = 20 − 10 20 = 0.5

3 5. Equation Equation A = ∑ (? 1,𝑖 − ? ̅ 1 )(? 𝑖 − ? ̅ ) 𝑁 𝑖=1 ∑ (? 𝑖 − ? ̅ 1 ) 2 𝑁 𝑖=1 Equation B = 𝜇̂ 1 − 𝜇̂ 2 se(𝜇̂ 1 − 𝜇̂ 2 ) Equation C = √ ∑ 𝜇̂ 𝑖 2 𝑁 𝑖=1 𝑁 Equation D = ? ̂ 1 𝜎 ̂ ? 𝜎 ̂ ? Equation E = √ ∑ 𝜇̂ 𝑖 2 𝑁 𝑖=1 𝑁 − 2 Match the quantity you wish to calculate with the correct equation. In each case ? and ? are continuous variables. i. The estimate of ? 1 in ? 𝑖 = ? + ? 1 ? 1,𝑖 + 𝜇 𝑖 [2] a. Equation A b. Equation B c. Equation C d. Equation D e. Equation E ii. The root mean squared error from estimating ? 𝑖 = ? + ? 1 ? 1,𝑖 + 𝜇 𝑖 [2] a. Equation A b. Equation B c. Equation C d. Equation D e. Equation E

4 5 continued Equation Equation A = ∑ (? 1,𝑖 − ? ̅ 1 )(? 𝑖 − ? ̅ ) 𝑁 𝑖=1 ∑ (? 𝑖 − ? ̅ 1 ) 2 𝑁 𝑖=1 Equation B = ∑ (? 𝑖 − ? ̅ )(? 𝑖 − ? ̅ ) 𝑁 𝑖=1 𝑁 Equation C = √ ∑ 𝜇̂ 𝑖 2 𝑁 𝑖=1 𝑁 Equation D = ? ̂ 1 𝜎 ̂ ? 𝜎 ̂ ? Equation E = √ ∑ 𝜇̂ 𝑖 2 𝑁 𝑖=1 𝑁 − 2 Match the quantity you wish to calculate with the correct equation. In each case ? and ? are continuous variables. iii. The covariance between ? and ? [2] a. Equation A b. Equation B c. Equation C d. Equation D e. Equation E iv. Standardizing the estimate of ? 1 in ? 𝑖 = ? + ? 1 ? 1,𝑖 + 𝜇 𝑖 [2] a. Equation A b. Equation B c. Equation C d. Equation D e. Equation E