Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q. R8.8 (page 548)

It’s about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.

a. Increasing the confidence level

b. Quadrupling the sample size

Short Answer

Expert verified

Part a) It could be said that an increase in the confidence level would lead increase in the margin of error.

Part b) it could be said that quadrupling the sample size would lead reduction in the margin of error.

Step by step solution

01

Part a) Step 1: Given information

All other things have remained constant.

02

Part a) Step 2: The objective is to explain the effect of the increase in the confidence level on the margin of error.

The margin of error is proportional to the confidence level, which means that an increase in confidence tends to increase the margin of error and vice versa.

Therefore, it could be said that an increase in the confidence level would lead increase in the margin of error.

03

Part b) Step 1: The objective is to explain the effect of quadrupling the sample size on the margin of error.

The margin of error is inversely proportional to the confidence level, which means that increasing the sample size reduces the margin of error and vice versa.

Therefore, it could be said that quadrupling the sample size would lead reduction in the margin of error.

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

Running red lights A random digit dialing telephone survey of 880 drivers asked, “Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?” Of the 880 respondents, 171 admitted that at least one light had been red.37

a. Construct and interpret a 95% confidence interval for the population proportion.

b. Nonresponse is a practical problem for this survey—only 21.6% of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: Do you think more or fewer than 171 of the 880 respondents really ran a red light? Why? Are these sources of bias included in the margin of error?

Got shoes? The class in Exercise 1 wants to estimate the variability in the number of pairs

of shoes that female students have by estimating the population standard deviation σ.

A school of fish Refer to Exercise 74.

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 packaging, there are supposed to be 330goldfish in each bag of crackers. Based on the interval, is there convincing evidence that the average number of goldfish is less than 330? Explain your answer.

Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.

a. We want to estimate the average age at which U.S. presidents have died. So we obtain a list of all U.S. presidents who have died and their ages at death.

b. Do teens text more than they call? To find out, an AP Statistics class at a large high school collected data on the number of text messages and calls sent or received by each of 25randomly selected students. The boxplot displays the difference (Texts − Calls) for each student.

Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?”
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision 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