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Chapter 8: Q.76 (page 520)
You have an SRS of observations from a Normally distributed population. What critical value would you use to obtain a confidence interval for the mean M of the population if S is unknown?
(a)
(b)
(c)
(d)
(e)
The correct option is (a).
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Hallux abducto valgus (call it HAV) is a deformation of the big toe that is fairly uncommon in youth and often requires surgery. Doctors used -rays to measure the angle (in degrees) of deformity in a random sample of patients under the age of who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. For these patients, the mean HAV angle was degrees and the standard deviation was degrees. A dot plot of the data revealed no outliers or strong skewness.
(a) Construct and interpret a confidence interval for the mean HAV angle in the population of all such patients.
(b) Researchers omitted one patient with an HAV angle of degrees from the analysis due to a measurement issue. What effect would including this outlier have on the confidence interval in (a)? Justify your answer.
How common is SAT coaching? A random sample of students who took the SAT college entrance examination twice found that of the respondents had paid for coaching courses and that the remaining had not. Construct and interpret a confidence interval for the proportion of coaching among students who retake the SAT. Follow the four-step process.
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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51. You want to design a study to estimate the proportion of students at your school who agree with the statement, 鈥淭he student government is an effective organization for expressing the needs of students to the administration.鈥� You will use a confidence interval, and you would like the margin of error to be or less. The minimum sample size required is
(a) . (b) . (c) . (d) . (e) .
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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