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Chapter 8: Q.7 (page 482)

NAEP scores Refer to Exercise 5. Below your sketch, choose one value of x inside the shaded region and draw its corresponding confidence interval. Do the same for one value of x outside the shaded region. What is the most important difference between these intervals?

Short Answer

Expert verified

The most important difference between these intervals

Step by step solution

01

Given Information

Model drawing:

02

Explanation

If the sample mean x¯lies in the shaded region, then the confidence interval will contain the true population mean μ.

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Most popular questions from this chapter

A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95%confidence margin of error of 3%. If the opinion poll had announced the margin of error for 80% confidence rather than 95%confidence, this margin of error would be

(a) 3%, because the same sample is used.

(b) less than 3%, because we require less confidence.

(c) less than 3%, because the sample size is smaller.

(d) greater than 3%, because we require less confidence.

(e) greater than 3%, because the sample size is smaller.

Teens and their TV setsAccording to a Gallup Poll report, 64% of teens aged 13to 17have 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 1028teenagers in the Gallup Poll Panel of households, aged 13to 17. For results based on this sample, one can say . . . that the maximum error attributable to sampling and other random effects is ±3percentage 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.16

(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.

It’s critical Find the appropriate critical value for constructing a confidence interval in each of the following settings.

(a) Estimating a population proportion p at a 94%confidence level based on an SRS of size 125.

(b) Estimating a population mean M at a 99%confidence level based on an SRS of size 58.

Refer to Exercise 12. As Gallup indicates, the 3percentage point margin of error for this poll includes only sampling variability (what they call “sampling error”). What other potential sources of error (Gallup calls these “non-sampling errors”) could affect the accuracy of the59% estimate?

What inference method will you use? Check that the conditions for using this procedure are met.
See all solutions

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