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Chapter 1: Q. 35 (page 52)

Is a sample of 500 volunteers a reliable measure for a population of 2,500?

Short Answer

Expert verified

Yes, for a population of 2500people, a sample size of500volunteers is a reliable metric.

Step by step solution

01

Introduction

When estimating unknown parameters, larger sample numbers often lead to greater precision. The rule of big numbers and the central limit theorem are two important principles of mathematical statistics that characterize this phenomena.

02

Explanation

A sample size of at least 10%of the population size is required.

Given a population of 2500people, the 10%would be 250.

As a result, a sample size of 250is a good estimate of the population parameter. Any sample size more than 250is also a good indicator.

For a population of 2500, a sample size of 500is a valid metric.

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Most popular questions from this chapter

1.13A local radio station has a fan base of 20,000listeners. The station wants to know if its audience would prefer

More music or more talk shows. Asking all 20,000listeners is an almost impossible task.

The station uses convenience sampling and surveys the first 200people they meet at one of the station鈥檚 music concert events. 24people said they鈥檇 prefer more talk shows, and 176 people said they鈥檇 prefer more music.

Do you think that this sample is representative of (or is characteristic of) the entire 20,000listener population?

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys six flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study.

a. Using complete sentences, list three things wrong with the way the survey was conducted.

b. Using complete sentences, list three ways that you would improve the survey if it were to be repeated.

List some practical difficulties involved in getting accurate results from a mailed survey.

Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

For the following four exercises, determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience).

A market researcher polls every tenth person who walks into a store.
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