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Chapter 1: Q14. (page 49)
Suppose that a production batch contains 1,000 units and you have to select 10 units for quality assurance. Use a random number generator to select a simple random sample of n = 10 from the production batch.
Sample:
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Explain how populations and samples differ?
Suppose you have to sort sample units into categories according to their region of origin. The regions are “Africa,” “Americas,” “Asia,” “Europe,” and “Oceania.” For further analysis with a statistical software, you replace each region name with a numerical code: 1 for Africa, 2 for Americas, and so on. Are the data consisting of the region names qualitative or quantitative? Are the numerical codes qualitative or quantitative? Explain your answer.
Current population survey. The employment status (employed or unemployed) of each individual in the U.S. workforce is a set of data that is of interest to economists, businesspeople, and sociologists. To obtain information about the employment status of the workforce, the U.S. Bureau of the Census conducts what is known as the Current Population Survey. Each month interviewers visit about 50,000 of the 117 million households in the United States and question the occupants over 14 years of age about their employment status. Their responses enable the Bureau of the Census to estimate the percentage of people in the labor force who are unemployed (the unemployment rate).
a. Define the population of interest to the Census Bureau.
b. What variable is being measured? Is it quantitative or qualitative?
c. Is the problem of interest to the Census Bureau descriptive or inferential?
d. In order to monitor the rate of unemployment, it is essential to have a definition of unemployed. Different economists and even different countries define it in various ways. Develop your own definition of an "unemployed person." Your definition should answer such questions as: Are students on summer vacation unemployed? Are college professors who do not teach summer school unemployed? At what age are people considered to be eligible for the workforce? Are people who are out of work but not actively seeking a job unemployed?
Can money spent on gifts buy love? Is the gift you purchased for that special someone really appreciated? This was the question of interest to business professors at Stanford University. Their research was published in the Journal of Experimental Social Psychology (Vol. 45, 2009). In one study, the researchers investigated the link between engagement ring price (dollars) and level of appreciation of the recipient (measured on a 7-point scale where 1 = “not at all” and 7 = “to a great extent”). Participants for the study were those who used a popular Web site for engaged couples. The Web site’s directory was searched for those with “average” American names (e.g., “John Smith,” “Sara Jones”). These individuals were then invited to participate in an online survey in exchange for a $10 gift certificate. Of the respondents, those who paid really high or really low prices for the ring were excluded, leaving a sample size of 33 respondents.
a. Identify the experimental units for this study.
b. What are the variables of interest? Are they quantitative or qualitative in nature?
c. Describe the population of interest.
d. Do you believe the sample of 33 respondents is representative of the population? Explain.
e. In a second designed study, the researchers investigated whether the link between gift price and level of appreciation is stronger for birthday gift-givers than for birthday gift-receivers. The participants were randomly assigned to play the role of gift-giver or gift-receiver. Assume that the sample consists of 50 individuals. Use a random number generator to randomly assign 25 individuals to play the gift-receiver role and 25 to play the gift-giver role.
The economic return to earning an MBA. What are the economic rewards (e.g., higher salary) to obtaining an MBA degree? This was the question of interest in an article published in the International Economic Review (August 2008). The researchers made inferences based on wage data collected for a sample of 3,244 individuals who sat for the Graduate Management Admissions Test (GMAT). (The GMAT exam is required for entrance into most MBA programs.) The following sampling scheme was employed. All those who took the GMAT exam in any of four selected time periods were mailed a questionnaire. Those who responded to the questionnaire were then sent three follow-up surveys (one survey every 3 months). The final sample of 3,244 represents only those individuals who responded to all four surveys. (For example, about 5,600 took the GMAT in one time period; of these, only about 800 responded to all four surveys.)
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.
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