Section 8.3 Confidence Intervals for a Population Proportion 389 result in complications. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.04? 306 b. Estimate the sample size needed if no estimate of p is available. 1037 Source: Journal of Bone and Joint Surgery 87:1719–1724 30. How’s the economy? A pollster wants to construct a 95% confidence interval for the proportion of adults who believe that economic conditions are getting better. a. A Gallup poll taken in February 2013 estimates this proportion to be 0.34. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.03? 958 b. Estimate the sample size needed if no estimate of p is available. 1068 31. Changing jobs: A sociologist sampled 200 people who work in computer-related jobs, and found that 42 of them have changed jobs in the past 6 months. a. Construct a 95% confidence interval for the proportion of those who work in computer-related jobs who have changed jobs in the past six months. (0.154, 0.266) b. Among the 200 people, 120 of them are under the age of 35. These constitute a simple random sample of workers under the age of 35. If this sample were used to construct a 95% confidence interval for the proportion of workers under the age of 35 who have changed jobs in the past six months, is it likely that the margin of error would be larger, smaller, or about the same as the one in part (a)? Larger 32. Political polling: A simple random sample of 300 voters was polled several months before a presidential election. One of the questions asked was: ‘‘Are you satisfied with the choice of candidates for president?’’ A total of 123 of them said that they were not satisfied. a. Construct a 99% confidence interval for the proportion of voters who are not satisfied with the choice of candidates. (0.337, 0.483) b. Among the 300 voters were 158 women. These constitute a simple random sample of women voters. If this sample were used to construct a 99% confidence interval for the proportion of women voters who are satisfied with the choice of candidates for president, is it likely that the margin of error would be larger, smaller, or about the same as the one in part (a)? Larger 33. Small sample: Eighteen concrete blocks were sampled and tested for crushing strength in order to estimate the proportion that were sufficiently strong for a certain application. Sixteen of the 18 blocks were sufficiently strong. Use the small-sample method to construct a 95% confidence interval for the proportion of blocks that are sufficiently strong. (0.657, 0.979) 34. Small sample: During an economic downturn, 20 companies were sampled and asked whether they were planning to increase their workforce. Only 3 of the 20 companies were planning to increase their workforce. Use the small-sample method to construct a 98% confidence interval for the proportion of companies that are planning to increase their workforce. (0.015, 0.401) 35. Calculator display: The following TI-84 Plus display presents a 99% confidence interval for a proportion. a. Fill in the blanks. We are confident that the population proportion is between and . 99%, 0.41911, 0.73714 b. Use the information in the display to construct a 95% confidence interval for p. (0.457, 0.699) 36. Calculator display: The following TI-84 Plus display presents a 95% confidence interval for a proportion. a. Fill in the blanks. We are confident that the population proportion is between and . 95%, 0.19525, 0.38253 b. Use the information in the display to construct a 98% confidence interval for p. (0.178, 0.400) 37. Computer output: The following MINITAB output presents a 98% confidence interval for a proportion. ������������ �� �� �� ������ ������ ������������ �� �� ������������ ����~ ���� .�� ������������, �� ������������/ a. Fill in the blanks. We are confident that the population proportion is between and . 98%, 0.732082, 0.870128 b. Use the information in the display to construct a 90% confidence interval for p. (0.752, 0.850) 38. Computer output: The following MINITAB output presents a 95% confidence interval for a proportion. ������������ �� �� ���� ���� �� ������������ �� �� ������������ ����~ ���� .�� ������������, �� ������������/ a. Fill in the blanks. We are confident that the population proportion is between and . 95%, 0.406111, 0.662854 b. Use the information in the display to construct a 99% confidence interval for p. (0.366, 0.703) 39. Don’t construct a confidence interval: The United States Senate consists of 100 senators. In January 2013, 20 of them were women. Explain why these data should not be used to construct a 95% confidence interval for the proportion of senators who are women. 40. Don’t construct a confidence interval: At the end of a television documentary on the nature of government, viewers are invited to tweet an answer to the question, ‘‘Do
navidi_monk_elementary_statistics_2e_ch7-9
To see the actual publication please follow the link above