/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 49. School vouchers A small pilot st... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q 49. (page 523)

School vouchers A small pilot study estimated 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.

a. How large a random sample is required to obtain a margin of error of at most 0.03with 99%confidence? Answer this question using the pilot study鈥檚 result as the guessed value for p^

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

Short Answer

Expert verified

a. n=1816

b. Increase in sample size is26.

Step by step solution

01

Given Information

It is given that E=0.03

p^=44%=0.44

02

Calculation of n

Sample size is p^known:n=za/22p^q^E2

=za/22p^(1-p^)E2

and p^unknown:n=za/220.25E2

Now for 1-伪=0.99, using table za/2=2.575

Hence, n=z伪/22p^(1-p^)E2

=2.5752脳0.44(1-0.44)0.032

n=1816

03

Increase in Sample Size

Asp^is known, hence

n=za/22p^(1-p^)E2

=2.5752脳0.50(1-0.50)0.032

n=1842

Difference between two sizes is 1842-1816=26

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Starting a nightclub A college student organization wants to start a nightclub for students under the age of 21.To assess support for this proposal, they will select an SRS of students and ask each respondent if he or she would patronize this type of establishment. What sample size is required to obtain a 90%confidence interval with a margin of error of at most 0.04?

The Large Counts condition When constructing a confidence interval for a population proportion, we check that both np鈭�andn1-p鈭�are at least 10

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?

Losing weight A Gallup poll asked a random sample of U.S. adults, 鈥淲ould you like to lose weight?鈥� Based on this poll, the 95%confidence interval for the population

proportion who want to lose weight is (0.56,0.62).

a. Interpret the confidence interval.

b. What is the point estimate that was used to create the interval? What is the margin of error?

c. Based on this poll, Gallup claims that more than half of U.S. adults want to lose weight. Use the confidence interval to evaluate this claim.

Refer to Exercise 55. Suppose that Gallup wanted to cut the margin of error in half from 3percentage points to 1.5percentage points. How should they adjust their sample size?

a. Multiply the sample size by 4.

b. Multiply the sample size by 2.

c. Multiply the sample size by 1/2.

d. Multiply the sample size by 1/4.

e. There is not enough information to answer this question.

Power lines and cancer Does living near power lines cause leukemia in

children? The National Cancer Institute spent 5years and $5million gathering data on this question. The researchers compared 638children who had leukemia with 620who did not. They went into the homes and measured the magnetic fields in children鈥檚 bedrooms, in other rooms, and at the front door. They recorded facts about power lines near the family home and also near the mother鈥檚 residence when she was pregnant. Result: No association between leukemia and exposure to magnetic fields of the kind produced by power lines was found.

a. Was this an observational study or an experiment? Justify your answer.

b. Does this study prove that living near power lines doesn鈥檛 cause cancer? Explain your answer.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.