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Chapter 1: Q9. (page 49)

What is a representative sample? What is its value?

Short Answer

Expert verified

The representative sample is the group that provides information on the entire population and is of great value for researchers and statisticians.

Step by step solution

01

Definition of a representative sample

A representative sample can be understood as the subset of the population that accurately indicates the attributes of the population considered for the study.

Example: Consider an organization with 500 employees bifurcated into 250 male employees and 250 female employees. Then the sample of 100 employees with 50 male and 50 female is an example of a representative sample.

02

Value of representative sample

The representative sample is important in statistics as it facilitatesacquiring information about the population just by studying the sample, which is a smaller group. For statisticians and researchers, studying details about the entire population is time-consuming; moreover, money and resources are spent on it; hence, studying the sample that comprises the characteristics of the entire population makes it easy and more convenient for them. Accordingly, the statistician can conclude and provide the required results in a shorter period along with utilizing lower resources.

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Most popular questions from this chapter

Treasury deficit prior to the Civil War. In Civil War History (June 2009), historian Jane Flaherty researched the condition of the U.S. Treasury on the eve of the Civil War in 1861. Between 1854 and 1857 (under President Franklin Pierce), the annual surplus/deficit was +18.8, +6.7, +5.3, and +1.3 million dollars, respectively. In contrast, between 1858 and 1861 (under President James Buchanan), the annual surplus/deficit was -27.3, -16.2, -7.2, and -25.2 million dollars, respectively. Flaherty used these data to aid in portraying the exhausted condition of the U.S. Treasury when Abraham Lincoln took office in 1861. Does this study represent a descriptive or inferential statistical study? Explain.

Structurally deficient highway bridges. Refer to Exercise 1.29. The NBI data were analyzed and the results made available at the FHWA Web site (www.fhwa.dot.gov). Using the FHWA inspection ratings, each of the 608,272 highway bridges in the United States was categorized as structurally deficient, functionally obsolete, or safe. About 13.5% of the bridges were found to be structurally deficient, while 3.5% were functionally obsolete.

a. What is the variable of interest to the researchers?

b. Is the variable of part a quantitative or qualitative?

c. Is the data set analyzed a population or a sample? Explain.

d. How did the NBI obtain the data for the study?

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A. For this study, describe the population of interest.

b. What method was used to collect the sample data?

c. Do you think the final sample is representative of the population? Why or why not? Comment on potential biases in the sample.

Stock prices. As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. They were then asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques.

a. Identify the population of interest for this study.

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d. Identify the sample of interest for this study.

e. Identify the experimental unit and variable of interest for this study.

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