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Chapter 8: Q. 41 (page 497)

A TV poll A television news program conducts a call-in poll about a proposed city ban on handgun ownership. Of the 2372 calls, 1921 oppose the ban. The station, following recommended practice, makes a confidence statement: "81%of the Channel 13 Pulse Poll sample opposed the ban. We can be 95% confident that the true proportion of citizens opposing a handgun ban is within1.6% of the sample result."

(a) Is the station's quoted 1.6% margin of error correct? Explain.

(b) Is the station's conclusion justifed? Explain.

Short Answer

Expert verified

a) No

b) No

Step by step solution

01

Part (a) Step1 : Given Information

Need to explain the margin of error quoted is1.6%

02

Part (a) Step2: Explanation

No, because the sample is a voluntary response sample, the confidence interval method's randomness condition is not met, and so the claimed1.6 percent margin of error is wrong.

03

Part (b) Step 2: Given Information 

Need to explain the stations conclusion.

04

Explanation(Part b)

No, because the sample is a voluntary response sample, the confidence interval method's randomization condition is not met, and hence the conclusion based on the confidence interval is erroneous.

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Most popular questions from this chapter

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 7days. How large a sample would be required to obtain a margin of error of 0.01ina99%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.

I collect an SRS of size n from a population and compute a 95%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. Approximately5% 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 0.05.

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.

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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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Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.

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