Log out Go to App
Go to App

Learning Materials

Features

Discover

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=Zα/2×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≥10: Here np^=2025×0.76=1539≥10andn(1-p^)=2025×(1-0.76)=486≥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=1.96×0.76(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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A 90%confidence interval for the mean μ of a population is computed from a random sample and is found to be90±30. Which of the following could be the 95%confidence interval based on the same data?

a. 90±21

b. 90±30

c. 90±39

d. 90±70

e. Without knowing the sample size, any of the above answers could be the 95%confidence interval.

A plethora of pepperoni? Refer to Exercise 73.

a. Explain why it was necessary to inspect a graph of the sample data when checking the Normal/Large Sample condition.

b. According to the manager of the restaurant, there should be an average of 40

pepperonis on a large pizza. Based on the interval, is there convincing evidence that the average number of pepperonis is less than 40? Explain your answer.

Reading scores in Atlanta The Trial Urban District Assessment (TUDA) is a

government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from 0to 500. A score of 243is a “basic” reading level and a score of 281is “proficient.” Scores for a random sample of 1470eighth-graders in Atlanta had a mean of 240with standard deviation of 42.17.

a. Construct and interpret a 99%confidence interval for the mean reading test score of all Atlanta eighth-graders.

b. Based on your interval from part (a), is there convincing evidence that the mean reading test score for all Atlanta eighth-graders is less than the basic level? Explain your answer.

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95%confidence and a margin of error no greater than 0.03. How large a random sample do we need?

Three branches According to a recent study by the Annenberg Foundation, only 36%of adults in the United States could name all three branches of government. This was based on a survey given to a random sample of1416U.S. adults.

a. Construct and interpret a 90%confidence interval for the proportion of all U.S. adults who could name all three branches of government.

b. Does the interval from part (a) provide convincing evidence that less than half of all U.S. adults could name all three branches of government? Explain your answer.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free