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Chapter 8: Q 42. (page 523)

September 11 A recent study asked U.S. adults to name 10historic events that occurred in their lifetime that have had the greatest impact on the country. The most frequently chosen answer was the September 11,2001, terrorist attacks, which was included by 76%of the 2025randomly selected U.S. adults. Construct and interpret a 95%confidence interval for the proportion of all U.S. adults who would include the 9/11attacks on their list of 10historic events.

Short Answer

Expert verified

For population proportion,95%confidence interval is0.7414<p<0.7786

Step by step solution

01

Given Information

It is given that n=2025

p^=76%=0.76

Confidence Level=0.95

02

Concept Used

Formula to be used:

p^=xn(Sample Proportion)

E=Z伪/2脳p^(1-p^)n(Margin of Error)

(p^-E,p^+E)(Confidence Interval)

03

Conditions

  • Random Selection: This is satisfied as US adults are selected randomly.
  • Less than 10% population: Adults are less than 10%of US adults. This condition is satisfied.
  • np^andn(1-p^)must be鈮�10: Here np^=2025脳0.76=1539鈮�10andn(1-p^)=2025脳(1-0.76)=486鈮�10which is met. This condition is also satisfied.

All conditions are met.

04

Calculation

Confidence level is 0.95

Level of significance is a=0.05

Zc=Za/2critical value=1.96

Margin of error is

E=1.96脳0.76(1-0.76)2025

Confidence interval is (0.76-0.0186,0.76+0.0186)

data-custom-editor="chemistry" (0.7414,0.7786)

E=0.0186

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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 7 days. How large a sample would be required to obtain a margin of error of at most 0.01 in a 99% confidence interval for the population proportion who would say that they attended a religious service?

More income The 2015American Community Survey estimated the median household income for each state. According to ACS, the 90%confidence interval for the 2015

median household income in New Jersey is \(72,222卤\)610.

a. Interpret the confidence interval.

b. Interpret the confidence level.

Teens and their TV sets According 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 卤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.

a. We omitted the confidence level from the footnote. Use what you have learned to estimate the confidence level, assuming that Gallup took an SRS.

b. Give an example of a 鈥減ractical difficulty鈥� that could lead to bias in this survey.

Fun size candyA candy bar manufacturer sells a 鈥渇un size鈥� version that is advertised to weigh 17grams. A hungry teacher selected a random sample of 44fun size bars and found a 95%confidence interval for the true mean weight to be 16.945grams to 17.395grams.

a. Does the confidence interval provide convincing evidence that the true mean weight is different than 17grams? Explain your answer.

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Got shoes? How many pairs of shoes, on average, do female teens have? To find out, an AP Statistics class selected an SRS of 20female students from their school.

Then they recorded the number of pairs of shoes that each student reported having. Here

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