Question

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.

Short answer

a. Engaged couples

b. The quantitative variable is the price of the engagement ring, and the qualitative variable is the level of appreciation.

c. Group of all engaged couples

d. No

e. Gift-receivers:$\left\{1,3,4,7,10,13,15,16,17,18,20,23,26,27,28,32,35,36,37,39,41,42,44,47,\left.49\right\}\right\}$

Gift-givers:$\left\{2,5,6,8,9,11,12,14,19,21,22,24,25,29,30,31,33,34,38,40,43,45,46,48,50\right\}$

Step-by-step solution

Identifying the experimental unit

The experimental unit of the research study must be the engaged couples.The research includes the price of engagement rings and the level of appreciation for which the professors of Stanford University must consider engaged couples.

Elucidating the variables

The engagement rings' price is considered quantitative as the price will be in numerical form. The level of appreciation is qualitative as appreciation always remains non-numerical.

Specifying the population of interest

The population of interest for this research study must be engaged couples using that website. By considering the engaged couples, the professors of Stanford can draw proper inferences.

Indicating False representation

The sample of 33 respondents will not represent the population of engaged couples. The website is visited by the unengaged persons also, and if they are chosen in the sample, then the inference drawn will not be reliable.

Using of random number generator

Here, randomly 25 numbers have been assigned to 25 gift-receivers, and another 25 numbers to another 25 individuals as shown below:

Gift-receivers:$\left\{1,3,4,7,10,13,15,16,17,18,20,23,26,27,28,32,35,36,37,39,41,42,44,47,49\right\}$

Gift-givers:$\left\{2,5,6,8,9,11,12,14,19,21,22,24,25,29,30,31,33,34,38,40,43,45,46,48,50\right\}$