Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q 35. (page 522)

Selling online According to a recent Pew Research Center report, many

American adults have made money by selling something online. In a random sample of 4579American adults, 914reported that they earned money by selling something online in the previous year. Assume the conditions for inference are met.

Determine the critical value z* for a 98% confidence interval for a proportion.

b. Construct a 98% confidence interval for the proportion of all American adults who

would report having earned money by selling something online in the previous year.

c. Interpret the interval from part (b).

Short Answer

Expert verified

a. The critical value for 98%confidence interval is 2.33

b. The confidence interval for proportion is 0.1859<p<0.2133

c. The confidence interval lie between0.1859and0.2133

Step by step solution

01

Given Information

It is given that x=914

n=4579

Confidence Level =0.98

Level of significance=0.02

02

Critical Value

Using EXCEL FORMULA=ABS(NORMSINV(0.02/2)), critical valueZC=2.33

03

To construct 98% confidence interval for a proportion

Sample Proportion p^=xn

p^=9144579=0.1996

Margin of Error E=Zα/2×p^(1-p^)n

E=2.33×0.1996(1-0.1996)4579

E=0.0137

Confidence Interval is (p^-E,p^+E)

(0.1996-0.0137,0.1996+0.0137)=(0.1859,0.2133)

98%confidence interval is0.1859<p<0.2133

04

Interpreting Confidence Interval

Based for given data and above calculations, there is 98%confidence that correct population proportion of American adults reported to earn money by selling online previous year lie between0.1859and0.2133.

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 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.

Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75%of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.

a. How large a sample must you test to estimate the proportion of PTC tasters within 0.04with 90%confidence? Answer this question using the 75%estimate 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?

The weights (in pounds) of three adult males are160,215and195. What is the standard error of the mean for these data?

a. 190

b. 27.84

c. 22.73

d. 16.07

e.13.13

California’s traffic People love living in California for many reasons, but traffic isn’t one of them. Based on a random sample of 572employed California adults, a 90%confidence interval for the average travel time to work for all employed California adults is 23minutes to 26 minutes.

a. Interpret the confidence level.

b. Name two things you could do to reduce the margin of error. What drawbacks do these actions have?

c. Describe how non response might lead to bias in this survey. Does the stated margin of error account for this possible bias?

Weeds among the corn Velvetleaf is a particularly annoying weed in cornfields. It produces lots of seeds, and the seeds wait in the soil for years until conditions are right for sprouting. How many seeds do velvetleaf plants produce? The histogram shows the counts from a random sample of 28plants that came up in a cornfield

when no herbicide was used. Determine if the Normal/Large Sample condition is met in this context.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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