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Chapter 8: Q.3.4 (page 511)
Interpret your interval in context.
There is probability that the mean healing rate is between and
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Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in bone mineral content (BMC) of the spines of randomly selected mothers during three months of breastfeeding. The mean change in BMC was and the standard deviation was .
(a) Construct and interpret a confidence interval to estimate the mean percent change in BMC in the population.
(b) Based on your interval from (a), do these data give good evidence that on average nursing mothers lose bone mineral? Explain.
Losing weight A Gallup Poll in November found that of the people in its sample said “Yes” when asked, “Would you like to lose weight?” Gallup announced: “For results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is percentage points.”
(a) Explain what the margin of error means in this setting.
(b) State and interpret the confidence interval.
(c) Interpret the confidence level.
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 difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.
(a) We omitted the confidence level from the footnote. Use what you have learned to determine the confidence level, assuming that Gallup took an SRS.
(b) Give an example of a “practical difficulty” that could lead to biased results for this survey.
The news article goes on to say: “The theoretical errors do not take into account a margin of additional error resulting from the various practical difficulties in taking any survey of public opinion.” List some of the “practical difficulties” that may cause errors in addition to the percentage point margin of error. Pay particular attention to the news article’s description of the sampling method.
School vouchers A national opinion poll found that % of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a small sample.
(a) How large an SRS is required to obtain a margin of error of (that is, ) in a % confidence interval? Answer this question using the previous poll’s result as the guessed value for .
(b) Answer the question in part (a) again, but this time use the conservative guess . By how much do the two sample sizes differ?
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