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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

Explain the difference between descriptive and inferential statistics.

Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on the problem was investigated in the Journal of Behavioral Decision Making (January 2007). A total of 171 volunteer students participated in the experiment, where each was randomly assigned to one of three emotional states (guilt, anger, or neutral) through a reading/writing task. Immediately after the task, the students were presented with a decision problem (e.g., whether or not to spend money on repairing a very old car). The researchers found that a higher proportion of students in the guilty-state group chose to repair the car than those in the neutral-state and anger-state groups.

a. Identify the population, sample, and variables measured for this study.

b. Identify the data-collection method used.

c. What inference was made by the researcher?

d. In later chapters you will learn that the reliability of an inference is related to the size of the sample used. In addition to sample size, what factors might affect the reliability of the inference drawn in this study?

Customer orders at a department store. A department store receives customer orders through its call center and website. These orders, as well as any special orders received in the stores are forwarded to a distribution center where workers pull the items on the orders from inventory, pack them, and prepare the necessary paperwork for the shipping company that will pick up the packages and deliver them to the customers. In order to monitor the subprocess of pulling the items from inventory, one order is checked every 15 minutes to determine whether the worker has pulled the correct item.

a. Identify the process of interest.

b. Identify the variable of interest. Is it quantitative or qualitative?

c. Describe the sample.

d. Describe the inference of interest.

e. How likely is the sample to be representative?

Drafting NFL quarterbacks. The National Football League (NFL) is a lucrative business, generating an annual revenue of about $8 million. One key to becoming a financially successful NFL team is drafting a good quarterback (QB) out of college. The NFL draft allows the worst-performing teams in the previous year the opportunity of selecting the best quarterbacks coming out of college. The Journal of Productivity Analysis (Vol. 35, 2011) published a study of how successful NFL teams are in drafting productive quarterbacks. Data were collected for all 331 quarterbacks drafted between 1970 and 2007. Several variables were measured for each QB, including draft position (one of the top 10 players picked, selection between picks 11 and 50, or selected after pick 50), NFL winning ratio (percentage of games won), and QB production score (higher scores indicate more productive QBs). The researchers discovered that draft position is only weakly related to a quarterback’s performance in the NFL. They concluded that “quarterbacks taken higher [in the draft] do not appear to perform any better.”

a. What is the experimental unit for this study?

b. Identify the type (quantitative or qualitative) of each variable measured.

c. Suppose you want to use this study to project the performance of future NFL QBs. Is this an application of descriptive or inferential statistics? Explain.

Explain how population and variables differ?
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