Question

Choosing portable grill displays. University of Maryland marketing professor R. W. Hamilton studied how people attempt to influence the choices of others by offering undesirable alternatives (Journal of Consumer Research, Mar. 2003). Such a phenomenon typically occurs when family members propose a vacation spot, friends recommend a restaurant for dinner, and realtors show the buyer potential homesites. In one phase of the study, the researcher had each of 124 college students select showroom displays for portable grills. Five different displays (representing five different-sized grills) were available, but only three would be selected. The students were instructed to select the displays to maximize purchases of Grill #2 (a smaller grill).a. In how many possible ways can the three-grill displays be selected from the 5 displays? List the possibilities.b. The next table shows the grill display combinations and number of each selected by the 124 students. Use this information to assign reasonable probabilities to the different display combinations.c. Find the probability that a student who participated in the study selected a display combination involving Grill #1.Grill Display CombinationNumber of Students1-2-3351-2-481-2-5422-3-442-3-512-4-534Based on Hamilton, R. W. "Why do people suggest what they do not want? Using context effects to influence others’ choices." Journal of Consumer Research, Vol. 29, Mar. 2003, Table.

Answer 1

Answer: The answer is given below

Step-by-step explanation:

a. In how many possible ways can the three-grill displays be selected from the 5 displays? List the possibilities.

For this question, we are going to use the combination rule. Check the attached file. After solving, we have 6 possibilities. They are:

1-2-3, 1-2-4, 1-2-5, 2-3-4, 2-3-5 and 2-4-5.

b. The probabilities of the combination are:

(1-2-3) = 35/124 = 0.282

(1-2-4) = 8/124 = 0.065

(1-2-5) = 42/124 = 0.339

(2-3-4) = 4/124 = 0.032

(2-3-5) = 1/124 = 0.008

(2-4-5) = 34/124 = 0.274

c. The probability that a student who participated in the study selected a display combination involving Grill #1 will be: P(1-2-3) + P(1-2-4) + P(1-2-5)

= 0.282 + 0.065 + 0.339

= 0.686

Check the attached file for further explanation.