Question 30

cal value for the confidence level you want. Use [a = 0.5 if you don't have a good idea about the value of f). 8.2 TECHNOLOGY CORNER TlNspire Instructions in Appendix B; HP Prime instructions on the book's Web site. 15. Confidence interval for a population proportion Section 8.2 EXBrClSBS For Exercises 27 to 30, check whether each of the condi- at his college. Thirtyeight of those interviewed think tions is met for calculating a confidence interval for the tuition is too high. populatm\" \"mom\" P' 29. AIDS and risk factors In the National AIDS Be- 27. Rating school food Latoya wants to estimate what havioral Surveys sample of 2673 adult heterosexuals, pg. proportion of the seniors at her boarding high school 0.2% had both received a blood transfusion and had 9 like the cafeteria food. She interviews an SRS of 50 a sexual partner from a group at high risk of AIDS. of the 175 seniors living in the dormitory. She nds We want to estimate the proportion p in the popula- that 14 think the cafeteria food is good. tion who share these two risk factors. 28. High tuition costs Glenn wonders what proportion 30. Whelks and mussels The small round holes you of the students at his school believe that tuition is too often see in sea shells were drilled by other sea high. He interviews an SRS of 50 of the 2400 students creatures, who ate the former dwellers of the shells. . . . Section 8.2 Estimating a Population Proportion 505 Whelks often drill into mussels, but this behavior 36. Teens' texting A Pew Internet and American Life appears to be more or less common in different STEP locations. Researchers collected whelk eggs from 4 Project survey found that 392 of 799 randomly selected teens reported texting with their friends the coast of Oregon, raised the whelks in the labora- every day. tory, then put each whelk in a container with some delicious mussels. Only 9 of 98 whelks drilled into a (a) Calculate and interpret a 95% confidence interval mussel."The researchers want to estimate the pro- for the population proportion p that would report portion p of Oregon whelks that will spontaneously texting with their friends every day. drill into mussels. (b) Is it plausible that the true proportion of American 31. 98% confidence Find z* for a 98% confidence teens who text with their friends every day is 0.45? pg 497 interval using Table A or your calculator. Show your Use your result from part (a) to support your answer. method. 37. Binge drinking Describe a possible source of error 32. 93%% confidence Find z* for a 93% confidence that is not included in the margin of error for the interval using Table A or your calculator. Show your 9% confidence interval in Exercise 35 method. 38. Teens' texting Describe a possible source of error 33. Going to the prom Tonya wants to estimate what that is not included in the margin of error for the proportion of her school's seniors plan to attend the 95% confidence interval in Exercise 36. prom. She interviews an SRS of 50 of the 750 seniors 39. How common is SAT coaching? A random sample in her school and finds that 36 plan to go to the 9 500 of students who took the SAT college entrance prom. examination twice found that 427 of the respondents (a) Identify the population and parameter of interest. had paid for coaching courses and that the remain- STEP (b) Check conditions for constructing a confidence 4 ing 2733 had not. "* Construct and interpret a 99% confidence interval for the proportion of coaching interval for the parameter. among students who retake the SAT. (c) Construct a 90% confidence interval for p. Show 40. 2010 begins In January 2010 a Gallup Poll asked a your method. STEP 4 random sample of adults, "In general, are you satisfied (d) Interpret the interval in context. or dissatisfied with the way things are going in the United States at this time?" In all, 256 said that they 34. Reporting cheating What proportion of students were satisfied and the remaining 769 said they were are willing to report cheating by other students? A not. Construct and interpret a 90% confidence inter- student project put this question to an SRS of 172 val for the proportion of adults who are satisfied with undergraduates at a large university: "You witness how things are going. two students cheating on a quiz. Do you go to the professor?" Only 19 answered "Yes."12 41. Equality for women? Have efforts to promote equal- ity for women gone far enough in the United States? (a) Identify the population and parameter of interest. A poll on this issue by the cable network MSNBC (b) Check conditions for constructing a confidence contacted 1019 adults. A newspaper article about the interval for the parameter. poll said, "Results have a margin of sampling error of (c) Construct a 9% confidence interval for p. Show plus or minus 3 percentage points."15 your method. (a) The news article said that 65% of men, but only 43% of women, think that efforts to promote equality d) Interpret the interval in context. have gone far enough. Explain why we do not have 35. Binge drinking In a recent National Survey of Drug enough information to give confidence intervals for pg 498 Use and Health, 2312 of 5914 randomly selected men and women separately. full-time U.S. college students were classified as binge drinkers. 13 (b) Would a 95% confidence interval for women alone