Choosing portable grill displays. Refer to the Journal of Consumer Research (March 2003) experiment on influencing the choices of others by offering undesirable alternatives, presented in Exercise. Recall that each of 124 college students selected three portable grills out of five to display on the showroom floor. The students were instructed to include Grill #2 (a smaller-sized grill) and select the remaining two grills in the display to maximize purchases of Grill #2. If the six possible grill display combinations (1–2–3, 1–2–4, 1–2–5, 2–3–4, 2–3–5, and 2–4–5) are selected at random, then the proportion of students selecting any display will be 1/6 =.167. One theory tested by the researcher is that the students will tend to choose the three-grill display so that Grill #2 is a compromise between a more desirable and a less desirable grill. Of the 124 students, 85 students selected a three-grill display that was consistent with that theory. Use this information to test the theory proposed by the researcher at α =.05.
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 Combination | Number of Students |
1-2-3 | 35 |
1-2-4 | 8 |
1-2-5 | 42 |
2-3-4 | 4 |
2-3-5 | 1 |
2-4-5 | 34 |
Based 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.
Experiment: | Observe the up face on a coin. |
Sample Space: | 1. Observe a head. |
2. Observe a tail. | |
This sample space can be represented in set notation as a set containing two sample points: S: {H, T} | |
Here, H represents the sample point Observe a head and T represents the sample point Observe a tail. | |
Experiment: | Observe the up face on a die. |
Sample Space: | 1. Observe a 1. |
2. Observe a 2. | |
3. Observe a 3. | |
4. Observe a 4. | |
5. Observe a 5. | |
6. Observe a 6. | |
This sample space can be represented in set notation as a set of six sample points: S: {1, 2, 3, 4, 5, 6 } | |
Experiment: | Observe the up faces on two coins. |
Sample Space: | 1. Observe hH. |
2. Observe HT. | |
3. Observe TH. | |
4. Observe TT. | |
This sample space can be represented in set notation as a set of four sample points: S: {HH, HT, TH, TT } | |
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