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Chapter 8: Q. 13 (page 482)

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 ±3percentage point margin of error. Pay particular attention to the news article’s description of the sampling method.

Short Answer

Expert verified

The practical difficulty is " Nonresponse bias is the result of not having data for everybody in the sample ".

Step by step solution

01

Given Information

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.

02

Explanation

Some of the practical difficulties:

Selection bias will exclude part of the population

Measurement of response bias will use a method that gives different values from the true value

Nonresponse bias is the result of not having data for everybody in the sample.

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Most popular questions from this chapter

In each of the following settings, check whether the conditions for calculating a confidence interval for the population proportion p are met.

1. An AP Statistics class at a large high school conducts a survey. They ask the first 100 students to arrive at school one morning whether or not they slept at least 8 hours the night before. Only 17 students say "Yes."

2. A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt.

A radio talk show host with a large audience is interested in the proportion pof adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100people who phoned in, 70answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?

I. The data are a random sample from the population of interest.

II. nis so large that both np⏞andn1-p⏞are at least 10.

III. The population is at least 10times as large as the sample.

(a) I only

(c) III only

(c) I, II, and III

(b) II only

(d) I and II only

Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology.

(a) A 98% confidence interval based on n=22observations.

(b) A 90%confidence interval from an SRS of 10observations.

(c) A 95% confidence interval from a sample of size7.

School vouchers A national opinion poll found that 44% 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 0.03(that is, ±3%) in a 99% confidence interval? Answer this question using the previous poll’s result as the guessed value for p∧.

(b) Answer the question in part (a) again, but this time use the conservative guess p∧=0.5. By how much do the two sample sizes differ?

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.
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