Statistics and Data Analysis Answer Key

Statistics & Data Analysis - Chapter 9 Multiple Choice AINSWERS The student newspaper at a college asks an SRS of 250 undergraduates, "Do you favor eliminating the carnival from the term-end celebration?" In all 150 of the 250 are in favor. The next four questions concern this sample survey. 3. The you want to estimate is the proportion p of all undergraduates who favor eliminating the carnival. (a) bias (b) confidence level (c) mean ( parameter (e) statistic 4. To estimate p, you will use the proportion hat p = 1.5/250 . of your sample who favored eliminating the carnival, The number p is a (a) bias (b) confidence level (c) mean (d) parameter (e) statistic 5. A 95% confidence interval for the population proportion pis (a) 180 plus/minus 0.03 (b) 0.6 plus/minus 0.03 (c) y * 50 plus/minus 0.06 d) 0.6 plus/minus 0.06 (e) y_{7} = 0.03 6. A 90% confidence interval based on this same sample would have (a) the some center and a larger margin of error. (b) the same center and a smaller margin of error. (c) a larger margin of error and probably a different center. (d) a smaller margin of error and probably-a-different center center will be same (e) the same margin of error and probably a different center. 70% 1645 9581.96 8. You want to estimate the proportion of undergraduates at a college who favor eliminating evening exams. You will choose an SRS. If you enlarge your SRS from 250 to 1000 students, the sample proportion (a) will have the same mean and the same stendfird deviation . (b) will have smaller this and the standard deviation will be 1/4 as large. sample size x4 (c) will have smallet bies and the standard deviation will be 1/2 as large. will have the same mean and the standard deviation will be 1/4 large (e) will have the same mean and the standard deviation will be 1/2 as large. 10. A recent Gallup Poll interviewed a random sample of 1523 adults. Of these, 868 bought a lottery ticket in the past year. A 95% confidence, interval for the proportion of all adults who bought a lottery ticket in the past year is (assume Gallup used an SRS) (+5451.5948 used calculator (a) 0.57 plus/minus 0.00016 ( b) 0.57 plus/minus 0.00032 (c 10.57 plus/minus 0.013 (d 0.57 plus/minus 0.025 (e) 0.57 plus/minus 0.03 11. Suppose that in fact (unknown to Gallup) exactly 60% of all adults bought a lottery ticket in the past year. If Gallup took many SRSs of 1523 people, the sample proportion who bought a ticket would vary from sample to sample. The sampling distribution would be close to normal with (8) mean 0.6 and standard deviation 0.00016 (b) mean 6.6 and standard deviation 0.0126 (c) mean 0.6 and standard deviation 0.4899 (d) mean 0.6 and standard deviation 0.0251 (e) mean 0.6 and standard deviation 0.0061 2.0126 12. The same Gallup Poll asked its 1523 adult respondents and also 501 teens (ages 13 to 17) whether they generally approved of legal gambling: 63% of adults and 52% of teens said yes. The margin of error for a 95% confidence Tätement about teens would be (a) greater than for adults, because the teen sample is smaller. (b) less than for adults, because the teen sample is smaller. (c) less them for adults, because there are fewer teens in the population. (d) the same as for adults, because they both come from the same sample survey. (e) can say, because it depends on what percent of each population was in the sample. sqrt((0.6(0.4))/250 \approx (0.03098)(1.96)) sqrt((0.6(0.4))/1523) 1/2 sqrt 4n A test of significance produces a P-value of 0.024. Which of the following conclusions is appropriate? (a) Reject Ho at the a 05 level; fail to reject at the a = 0.01 level. (B) Reject He at both the .05 level and the a = 0.01 level. (c) Fail to reject Ho at the level and reject at the 01 level. alpha = 0.05 P.2 024<.05 024.05 rejest Ho Fail to reject at 27. 01 (d) Fail to reject at both the level and the a01 level. a = 0.05 (e) No conclusions can be drawn on the basis of this P-value 17. The null hypothesis is (a) another name for the-effernative hypothesis (b) true with 95% probability (c) usually a statement of "no effect" or "no difference" (e) statistically significant 18. If a significance test gives a P-value of 0.50, 50% (d) determined by looking at the data fal the margin of error is 0.50 (b) the null hypothesir is very likely to be true (c) we do not have good evidence against the null hypothesis (d) we do have good evidence against the null hypothesis (c) the effect of interest is practically significant 20. If a significance test gives P-value 0.005, (a) the margin af error is 0.005. (b) the null hypothesis is very ffkely to be true. we do not have good evidence against the null hypothesis. (d) we do have good evidence arainst the mill hypothesis. Reject Ho (e) the effect of interest is practically significant. 21. The report of a sample survey of 1,014 adults says, "With 95% confidence, between 9% and 15% of all Americans expect to spend more money on gifts this year than last year. The phrase "95% confidence" means (a) 95% of all Americans will spend between 9% and 15% of what they spent last year. (b) 9% to 15% of all Americans will spend 95% of what they spent last year. (c) there is a 95% chance that the percent who expect to spend more is between 9% and 15%. (d) The method used to get the interval from 9% to 15%, when used over and over, produces intervals which include the tre population perventage 95% of the time. we can be 95% confident that the method used to get the interval always ves the right answer. 22. A sample survey finds that 30% of a sample of 874 Ohio adults said good health was the thing they thankful for. If that sample were an SRS from the population of all Ohio adults, what would be the 99% confidence interval for the percent of all Qhio-adults who feel that way? (a) 25% to 35% 26% 10 34% (c) 27% to 33% (d) 28% to 32% ( The name for the pattern of values-that-a statistic takes when we sample repeatedly from the same population ins 2599). 3397) used calculator (c) 29% to 31% 24. (a) the bias of the statistic. (b) the sampling distribution of the statistic. (c) the scale of measurement of the statistic (d) the variability of the statistic. (e) the sampling error. 28. A CBS News/New York Times opinion poll asked 1.190 adults whether they would prefer balancing the Federal budget over cutting taxes; 702 of those asked said "Yes." Take the sample to be an SRS from the population of all adults, Which of these is a correct 95% confidence interval for the proportion of all adults who prefer balancing the budget over cutting taxes? (a) 0.590.0004 (e) 0.39 (c) 0.39 0.037 (b) 0.59 0.014 (d)0.59 ± 0.0279 29. Suppose that in fact 62% of all adults favor balancing the-budget over-cutting taxes. The number 62% is ( a) a bias. (b) a margin of error. (c) a statistic. (d) a parameter (e) a coefficient of variation. 0.56 = 0j * 0.6179 ) 0.3 plus/minus 2.576 * sqrt((0.3(0.7))/874)