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Chapter 8: Q. 37 (page 496)
Abstain from drinking Describe a possible source of error that is not included in the margin of error for the confidence interval in Exercise
There are possible sources of errors.
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I collect an SRS of size n from a population and compute a confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?
(a) Use a larger confidence level.
(b) Use a smaller confidence level.
(c) Increase the sample size.
(d) Use the same confidence level, but compute the interval n times. Approximately of these intervals will be larger.
(e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is .
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.
The news article goes on to say: 鈥淭he 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.鈥� List some of the 鈥減ractical difficulties鈥� that may cause errors in addition to the percentage point margin of error. Pay particular attention to the news article鈥檚 description of the sampling method.
NAEP scores Refer to Exercise 5. Below your sketch, choose one value of inside the shaded region and draw its corresponding confidence interval. Do the same for one value of outside the shaded region. What is the most important difference between these intervals?
Do you go to church? The Gallup Poll plans to ask a random sample of adults whether they attended a religious service in the last days. How large a sample would be required to obtain a margin of error of confidence interval for the population proportion who would say that they attended a religious service? Show your work.
- Construct and interpret a confidence interval for a population proportion.
- Explain how practical issues like nonresponse, under coverage, and response bias can affect the interpretation of a confidence interval.
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