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Chapter 8: Q.27 (page 496)
Rating dorm food Latoya wants to estimate what proportion of the seniors at her high school like the cafeteria food. She interviews an SRS of of the seniors living in the dormitory. She finds that think the cafeteria food is good.
All three conditions for confidence interval is not satisfied
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Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of tires was obtained. Both methods were used to estimate the total distance traveled by each tire. The table below provides the two estimates (in thousands of miles) for each tire.
(a) Construct and interpret a confidence interval for the mean difference in the estimates from these two methods in the population of tires.
(b) Does your interval in part (a) give convincing evidence of a difference in the two methods of estimating tire wear? Justify your answer.
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Power lines and cancer Does living near power lines cause leukemia in children? The
National Cancer Institute spent 5 years and million gathering data on this question. The researchers compared children who had leukemia withwho did not. They went into the homes and actually measured the magnetic fields in children's bedrooms, in other rooms, and at the front door. They recorded facts about power lines near the family home and also near the mother's residence when she was pregnant. Result: no connection between leukemia and exposure to magnetic fields of the kind produced by power lines was found.
(a) Was this an observational study or an experiment? Justify your answer.
(b) Does this study show that living near power lines doesn't cause cancer? Explain.
63. Give it some gas! Computers in some vehicles calculate various quantities related to performance. One of these is fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle
equipped in this way, the miles per gallon were recorded each time the gas tank was filled and the computer was then reset. Here are the mpg values for a random sample of of these records:
Construct and interpret a confidence interval for the mean fuel efficiency M for this vehicle.
34. Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of undergraduates at a large university: 鈥淵ou witness two students cheating on a quiz. Do you go to the professor?鈥� Only answered 鈥淵es.鈥�
(a) Identify the population and parameter of interest.
(b) Check conditions for constructing a confidence interval for the parameter.
(c) Construct a confidence interval for. Show your method.
(d) Interpret the interval in context.
Teens and their TV setsAccording to a Gallup Poll report, % of teens aged to have TVs in their rooms. Here is part of the footnote to this report:
These results are based on telephone interviews with a randomly selected national sample of teenagers in the Gallup Poll Panel of households, aged to . For results based on this sample, one can say . . . that the maximum error attributable to sampling and other random effects is percentage points. In addition to sampling error, question-wording and practical dif铿乧ulties in conducting surveys can introduce error or bias into the 铿乶dings of public opinion polls.
(a) We omitted the con铿乨ence level from the footnote. Use what you have learned to determine the con铿乨ence level, assuming that Gallup took an SRS.
(b) Give an example of a 鈥減ractical dif铿乧ulty鈥� that could lead to biased results for this survey.
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