Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q4 (page 350)

Loose Change USA Todayreported that 40% of people surveyed planned to use accumulated loose change for paying bills. The margin of error was given as ±3.1 percentage points. Identify the confidence interval that corresponds to that information.

Short Answer

Expert verified

The confidence interval that corresponds to the provided information is 36.9% < p < 43.1%.

Step by step solution

01

Given information

The percentage of people who planned to use accumulated loose change for paying bills is 40%.

The margin of error is ±3.1percentage points.

02

Compute the confidence interval

From the given information, the following points can be concluded:

The proportion of people who planned to use accumulated loose change for paying bills is p^=0.40.

The margin of error is E=0.031.

The confidence interval is computed as follows:

(p^-E,p^+E)=0.40-0.031,0.40+0.031=0.369,0.431

Therefore, the confidence interval is36.9% < p < 43.1%.

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

Confidence Intervals. In Exercises 9–24, construct the confidence interval estimate of the mean.

In a study of speed dating conducted at Columbia University, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Use a 99% confidence level. What do the results tell us about the mean attractiveness ratings made by the population of all adult females?

7 8 2 10 6 5 7 8 8 9 5 9

Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12oz of drink) obtained in one can from each of 20 brands (7UP, A&W root Beer, Cherry Coke, …TaB). Use a confidence interval 99%. Does the confidence interval give us good information about the population of all cans of the same 20 brands that are consumed? Does the sample appear to be from a normally distributed population? If not, how are the results affected?

0 0 34 34 34 45 41 51 55 36 47 41 0 0 53 54 38 0 41 47

Coping with No Success: According to the Rule of Three, when we have a sample size n with x = 0 successes, we have 95% confidence that the true population proportion has an upper bound of 3/n. (See “A Look at the Rule of Three,” by Jovanovic and Levy, American Statistician, Vol. 51, No. 2.)a. If n independent trials result in no successes, why can’t we find confidence interval limits by using the methods described in this section? b. If 40 couples use a method of gender selection and each couple has a baby girl, what is the 95% upper bound for p, the proportion of all babies who are boys?

Online Buying In a Consumer Reports Research Centre survey, women were asked if they purchase books online, and responses included these: no, yes, no, no. Letting “yes” = 1 and letting “no” = 0, here are ten bootstrap samples for those responses: {0, 0, 0, 0}, {1, 0, 1, 0}, {1, 0, 1, 0}, {0, 0, 0, 0},{0, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 1, 0, 0}, {1, 1, 0, 0}. Using only the ten given bootstrap samples, construct a 90% confidence interval estimate of the proportion of women who said that they purchase books online.

In Exercises 1–3, refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 “Airport Data Speeds” in Appendix B. The confidence level of 95% was used.

Interpreting a Confidence Interval The results in the screen display are based on a 95%confidence level. Write a statement that correctly interprets the confidence interval.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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