Statistical Analysis: Hypothesis Testing for Proportions and Differences of Means, Exams of Statistics

Download Statistical Analysis: Hypothesis Testing for Proportions and Differences of Means and more Exams Statistics in PDF only on Docsity! STA3032 Section 7661 EXAM 2. (Nov. 18th, 2008) Name: UFID#: 1-4 A vote is to be taken among the residents of a town and the surrounding suburbs to determine whether an oil refinery should be constructed. The construction site is within the town limits and because of the large proportion of town voters who favor the construction, many voters in the suburbs fell that the proposal will pass. To determine if there is a significant difference in the proportion of town voters and suburban voters who favor the proposal, a poll is taken. The summary statistics are given in the following table. Would you agree that the proportion of town voters who favor the proposal is higher than the proportion of suburban voters? Let p1 and p2 be the true proportion of voters in the town and its suburbs, respectively, who favor the proposal. Use a 0.025 level of significance (α = 0.025). Town Voters Suburban Voters Sample size 200 500 Number of voters who favor the proposal 120 240 p̂ 0.600 0.480 p̃ 0.599 0.480 1. Choose the most appropriate set of hypothesis for this test. (1 points) (a) H0 : p1 − p2 = 0 vs. H1 : p1 − p2 > 0 (b) H0 : p1 − p2 6= 0 vs. H1 : p1 − p2 > 0 (c) H0 : p1 − p2 > 0 vs. H1 : p1 − p2 6= 0 (d) H0 : p1 − p2 < 0 vs. H1 : p1 − p2 6= 0 1 2. What is the value of the test statistics? (2 points) (a) 2.911 (b) 2.870 (c) 0.514 (d) 0.120 3. What is the p − value and the conclusion of this test? (2 points) (a) p − value = 0.0041, reject H0 (b) p − value = 0.0041, fail to reject H0 (c) p − value = 0.00205, fail to reject H0 (d) p − value = 0.00205, reject H0 4. What is the calculated 95% confidence interval for p1 − p2? (2 points) (a) (0.039, 0.199) (b) (0.051, 0.187) (c) (0.052, 0.188) (d) (0.041, 0.197) 5. From the previous study, we could get prior information that a guess of the population proportion is p∗ = 0.12. What is the sample size if we want to estimate the true population proportion to within 0.05, with 95% confidence? (2 points) (a) 163 (b) 159 (c) 381 (d) 385 2 11-18 Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (X) and pavement deflection (Y ). The summary of data is given in the following table: X (Temperature) Y (Deflection) mean 73.185 0.637 standard deviation 2.554 0.011 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) (11) 0.0425840 9.240 2.97e-08 *** X 0.0033285 0.0005815 (12) 1.99e-05 *** --- Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1 Residual standard error: 0.006473 on 18 degrees of freedom Analysis of Variance Table Response: Y Df Sum Sq Mean Sq F value Pr(>F) X 1 0.00137271 (14) (15) (16) Residuals (13) 0.00075424 0.00004190 11. What is the computed value of (11)? (2 points) (a) 0.393 (b) 0.006 (c) 0.003 (d) 0.001 5 12. What is the computed value of (12)? (2 points) (a) 9.240 (b) 3.131 (c) 2.878 (d) 5.724 13. What is the value of (13)? (1 points) (a) 19 (b) 18 (c) 17 (d) 16 14. What is the computed value of (14)? (2 points) (a) 0.00137271 (b) 0.00075424 (c) 0.00004190 (d) 0 15. What is the computed value of (15)? (2 points) (a) 1.820 (b) 32.762 (c) 5.724 (d) 3.312 6 16. What is the p-value in (16) and the right conclusion? The significant level α = 0.05. (2 points) (a) p − value < 0.01, fail to reject H0 : β1 = 0 . (b) p − value < 0.02, reject H0 : β0 = 0. (c) p − value < 0.01, reject H0 : β1 = 0. (d) p − value < 0.02, fail to reject H0 : β0 = 0. (e) None of the above 17. What is the value of the Coefficient of Determination R2 and the right interpretation? (3 points) (a) R2 = 0.970: 97% of the variation of the roadway surface temperature is explained by the pavement deflection. (b) R2 = 0.970: 97% of the variation of pavement deflection is explained by the roadway surface temperature. (c) R2 = 0.645: 64.5% of the variation of the roadway surface temperature is ex- plained by the pavement deflection. (d) R2 = 0.645: 64.5% of the variation of pavement deflection is explained by the roadway surface temperature. 18. What is the 95% prediction interval for pavement deflection with the roadway surface temperature 78? sby = 0.00315207. (2 points) (a) (0.641, 0.665) (b) (0.640, 0.666) (c) (0.638, 0.668) (d) (0.446, 0.860) 7