Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q5 (page 354)

Critical Thinking: What does the survey tell us? Surveys have become an integral part of our lives. Because it is so important that every citizen has the ability to interpret survey results, surveys are the focus of this project. The Pew Research Center recently conducted a survey of 1007 U.S. adults and found that 85% of those surveyed know what Twitter is.

Analyzing the Data

A common criticism of surveys is that they poll only a very small percentage of the population and therefore cannot be accurate. Is a sample of only 1007 adults taken from a population of all adults a sample size that is too small? Write a brief explanation of why the sample size of 1007 is or is not too small.

Short Answer

Expert verified

Surveys involving large populations assume a sample size of 1000 units. Thus, the sample size of this survey, equal to 1007 adults, is adequate and not too small.

Step by step solution

01

Given information

A survey consisted of 1007 U.S. adults. 85% of those who were surveyed know what Twitter is.

02

Adequacy of the sample size

It is generally believed that for a survey involving an extremely large population (nationwide/worldwide individuals), a sample size of 1000 units is considered sufficient.

A sample size greater than 1000 units will incur significantly high costs and time intake. Thus, a size greater than 1000 units is not desirable.

Here, the population considered is the population of all adults (very large).

The sample size considered is equal to 1007 adults (approximately equal to 1000).

Therefore, the sample size of 1007 adults to conduct the survey is adequate.

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

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?

Finding Critical Values In constructing confidence intervals for σor σ2, Table A-4 can be used to find the critical values χL2and χR2only for select values of n up to 101, so the number of degrees of freedom is 100 or smaller. For larger numbers of degrees of freedom, we can approximate χL2andχR2 by using,

χ2=12±zα2+2k-12

where k is the number of degrees of freedom and zα2is the critical z score described in Section 7-1. Use this approximation to find the critical values χL2and χR2for Exercise 8 “Heights of Men,” where the sample size is 153 and the confidence level is 99%. How do the results compare to the actual critical values of χL2= 110.846 and χR2= 200.657?

Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from “Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults,” by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population and construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments. What does the result suggest about the mean wake time of 102.8 min before the treatment? Does zopiclone appear to be effective?

Bootstrap Sample.

Here is a random sample of taxi-out times (min) for American Airlines flights leaving JFK airport: 12, 19, 13, 43, 15. For this sample, what is a bootstrap sample?

Celebrities and the Law Here is a 95% confidence interval estimate of the proportion of adults who say that the law goes easy on celebrities: 0.692 <p< 0.748 (based on data from a Rasmussen Reports survey). What is the best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure 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