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Chapter 8: Q. 14 (page 482)

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

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

As Gallup indicates, the 3percentage point margin of error for this poll includes only sampling variability

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

A Census Bureau report on the income of Americans says that with 90% confidence the median income of all U.S. households in a recent year was \(57,005 with a margin of error of 卤\)742. This means that

(a) 90% of all households had incomes in the range \(57,005 卤\)742.

(b) we can be sure that the median income for all households in the country lies in the range \(57,005 卤\)742.

(c) 90% of the households in the sample interviewed by the Census Bureau had incomes in the range \(57,005 卤\)742.

(d) the Census Bureau got the result \(57,005 卤\)742 using a method that will cover the true median income 90% of the time when used repeatedly.

(e) 90% of all possible samples of this same size would result in a sample median that falls within \(742 of \)57,005.

Define the parameter of interest.

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, 卤3%) in a 99% con铿乨ence interval? Answer this question using the previous poll鈥檚 result as the guessed value for p鈭�.

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

Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams/liter) near the top and the bottom of 10randomly selected wells in a large region. The data are provided in the table below.

(a) Construct and interpret a 95%confidence interval for the mean difference 渭in the zinc concentrations from these two locations in the wells.

(b) Does your interval in part (a) give convincing evidence of a difference in zinc concentrations at the top and bottom of wells in the region? Justify your answer.

Watching TV (6.1, 7.3) Choose a young person (aged 19to 25) at random and ask, 鈥淚n the past seven days, how many days did you watch television?鈥� Call the response Xfor short. Here is the probability distribution for X.

(a) What is the probability that X=7? Justify your answer.

(b) Calculate the mean of the random variable X. Interpret this value in context.

(c) Suppose that you asked 100randomly sele

cted young people (aged 19to 25) to respond to the question and found that the mean xof their responses was 4.96. Would this result surprise you? Justify your answer.

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