/*! 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. 11.71 In this Exercise, we have given ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Q. 11.71 (page 462)

In this Exercise, we have given the number of successes and the sample size for a simple random sample from a population. In each case,

a. use the one-proportion plus-four z-interval procedure to find the required confidence interval.

b. compare your result with the corresponding confidence interval found in Exercise 11.25-11.30, if finding such a confidence interval was appropriate.

role="math" localid="1651327118166" x=35,n=50,99%level

Short Answer

Expert verified

(a) The one-proportion z-interval technique is adequate because xand n-xare both 5or more.

(b) It is possible to be 90%certain that the confidence interval is between 0.533and 0.867.

Step by step solution

01

Part(a) Step 1: Given Information

The size of a simple random sample from a population, as well as the number of successes.

x=35,n=50,99%level

鈭�n-x=50-35=15, here xand n-x are both 5 or greater.

02

Part(a) Step 2: Explanation

The sample proportion p'=xnis calculated from the data.

3550=0.7

03

Part(b) Step 1: Given Information

The size of a simple random sample from a population, as well as the number of successes.

x=35,n=50,99%level

鈭�n-x=50-35=15, here xand n-x are both 5 or greater.

04

Part(b) Step 2: Explanation

The confidence interval is 95%, which means 伪=0.05.

It is discovered thatza/2=z0.01/2=2.576

The pconfidence interval is of the form

p'-za/2p'1-p'ntop'+za/2p'1-p'n

i.e. role="math" localid="1651328225031" 0.7-2.5760.7(1-0.7)50to0.7+2.5760.7(1-0.7)50

i.e. (0.7-0.167)to(0.7+0.167)

i.e.0.533to0.867

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

What does the margin of error for the estimate of a population proportion tell you?

a. Determine the sample proportion.

b. Decide whether using the one-proportion z-test is appropriate.

c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.

x=3

n=100

H0:p=0.04

Ha:p鈮�0.04

伪=0.10

11.91 Economic Stimulus. In a national poll, 1053 U.S. adults were asked, "As you may know, Congress is considering a new economic stimulus package of at least 800 billion dollars. Do you favor or oppose Congress passing this legislation?" Of those sampled, 548 favored passage.
a. At the 5% significance level, do the data provide sufficient evidence to conclude that a majority (more than 50% ) of U.S. adults favored passage?
b. The headline on the website featuring the survey read, "In U.S., Slim Majority Supports Economic Stimulus Plan." In view of your result from part (a), discuss why the headline might be misleading.
c. How could the headline be made more precise?

Suppose that you can make reasonably good educated guesses, p^1gand p^2g, for the observed values of p^1and p^2.

a. Use your result from Exercise 11.132to show that a (1-伪)-level confidence interval for the difference between two population proportions that has an approximate margin of error of Ecan be obtained by choosing

n1=n2=p^1g1-p^1g+p^2g1-p^2gza/2E2

rounded up to the nearest whole number. Note: If you know likely ranges instead of exact educated guesses for the observed values of the two sample proportions, use the values in the ranges closest to 0.5as the educated guesses.

b. Explain why the formula in part (a) yields smaller (or at worst the same) sample sizes than the formula in Exercise 11.133.

c. When reasonably good educated guesses for the observed values of p^1and p^2can be made, explain why choosing the sample sizes by using the formula in part (a) is preferable to choosing them by using the formula in Exercise 11.133.

Margin of error =0.01

Confidence level=95%

Educated guess =0.3

(a) Obtain a sample size that will ensure a margin of error of at most the one specified (provided of course that the observed value of the sample proportion is further from 0.5that of the educated guess.

(b). Compare your answer to the corresponding one and explain the reason for the difference, if any.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete 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.