Review Questions Module 12

Review Questions Module 12 1. In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately (a) 0.03 (b) 0.25 (c) 0.0094 (d) 6.12 (e) 0.06 (f) None of the above. The answer is _____________________________. 2. You want to design a study to estimate the proportion of students on your campus who agree with the statement, “The student government is an effective organization for expressing the needs of students to the administration.” You will use a 95% confidence interval and you would like the margin of error to be 0.05 or less. The minimum sample size required is approximately (a) 22 (b) 1795 (c) 385 (d) 271 (e) None of the above. The answer is _____________________________. 3. An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are: (a) H 0 : p̂ = 0.5; H a : p̂ > 0.5 (b) H 0 : p̂ = 0.5; H a : p̂ ≠ 0.5 (c) H 0 : p = 0.5; H a : p ≠ 0.5 (d) H 0 : p = 0; H a : p > 0 (e) H 0 : p = 0.5; H a : p > 0.5 4. A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out he poses the following question to his listeners. “Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteenyear-olds are eligible for military service?” He asks listeners to phone in and vote “yes” if they agree the drinking age should be lowered and “no” if not. Of the 100 people who phoned in 70 answered “yes.” Which of the following conditions for inference about a proportion using a confidence interval are violated? (a) The data are an SRS from the population of interest. (b) The population is at least ten times as large as the sample. (c) n is so large that both the count of successes n p and the count of failures n(1 – p) are ten or more. (d) There appear to be no violations. (e) More than one condition is violated. 5. A polling organization announces that the proportion of American voters who favor congressional term limits is 64 %, with a 95% confidence margin of error of 3 %. This means that (a) If the poll were conducted again in the same way, there is a 95% chance that the fraction of voters favoring term limits in the second poll would be between 61 % and 67 %. (b) There is a 95% probability that the true percentage of voters favoring term limits is between 61 and 67%. (c) If the poll were conducted again the same way, there is a 95% probability that the percentage of voters favoring term limits in the second poll would be within 3 % of the percentage favoring term limits in the first poll. (d) Among 95% of the voters, between 61 % and 67 % favor term limits. (e) We are 95% confident that the true percentage of voters favoring term limits is between 61 and 67%. 6. An SRS of size 100 is taken from a population having proportion 0.8 successes. An independent SRS of size 400 is taken from a population having proportion 0.5 successes. The sampling distribution of the difference in sample proportions has what mean? (a) 0.3 (b) 0.15 (c) The smaller of 0.8 and 0.5 (d) The mean cannot be determined without the sampling results. (e) None of the above. The answer is _____________________________. 7. This is a continuation of Problem 6. The sampling distribution for the difference in sample proportions has what standard deviation? (a) 1.3 (b) 0.40 (c) 0.047 (d) 0.0002 (e) None of the above. The answer is _____________________________. 8. Some scientists believe that a new drug would benefit about half of all people with a certain blood disorder. To estimate the proportion of patients who would benefit from taking the drug, the scientists will administer it to a random sample of patients who have the blood disorder. What sample size is needed so that the 95% confidence interval will have a width of 0.06? (a) 748 (b) 1,068 (c) 1,503 (d) 2,056 (e) 2,401 ≥ 9. The college newspaper of a large southern university periodically conducts a survey of students on campus to determine the attitude on campus concerning issues of interest. Pictures of the students interviewed along with quotes of their responses are printed in the paper. Students are interviewed by a reporter “roaming” the campus selecting students to interview “haphazardly.” On a particular day the reporter interviews five students and asks them if they feel there is adequate student parking on campus. Four of the students say no. Which of the following conditions for inference about a proportion using a confidence interval are violated in this example? (a) The data are an SRS from the population of interest. (b) The population is at least ten times as large as the sample. (c) np̂ 10 and n(1 − p̂) ≥ 10 . (d) We are interested in inference about a proportion. (e) More than one condition is violated. 10. In a test of H0: p = 0.4 against Ha: p ≠ 0.4, a sample of size 100 produces z = 1.28 for the value of the test statistic. Thus the P-value (or observed level of significance) of the test is approximately equal to: (a) 0.90 (b) 0.40 (c) 0.05 (d) 0.20 (e) 0.10 Answers: 1. A, 2. C, 3. E, 4. A, 5. E, 6. A, 7. C, 8. B, 9. E, 10. D