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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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