Chapter 1: Q9. (page 49)
What is a representative sample? What is its value?
The representative sample is the group that provides information on the entire population and is of great value for researchers and statisticians.
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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?
Explain how populations and samples differ?
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 “lucky store effect” in lottery ticket sales. In the American Economic Review (Vol. 98, 2008), University of Chicago researchers investigated the lucky store effect theory in lottery ticket sales, i.e., the theory that a lottery retail store that sold a large-prize-winning ticket will experience greater ticket sales the following week. The researchers examined the weekly ticket sales of all 24,400 active lottery retailers in Texas. The analysis showed that “the week following the sale of [a winning Lotto Texas ticket], the winning store experiences a 12 to 38 percent relative sales increase. . . . ” Consequently, the researchers project that future winning lottery retail stores will experience the lucky store effect. Is this study an example of descriptive statistics or inferential statistics? 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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