In: Statistics and Probability
Problem Set 1: (15 pts) Research Scenario: The following scenario is based loosely on an actual study conducted in 2013 by Ahn, Kim, and Aggarwal– please note that methods and data have been modified for educational purposes.
Do you turn off the light when you leave the room? South Korean researchers wondered how they could increase the number of people who do by use of posters (Ahn, Kim, & Aggarwal, 2013). In one, an image of a light bulb was anthropomorphized by giving it eyes, nose, and a mouth, as well as adding the words, “I’m burning hot, turn me off when you leave!”. In a second, there were no human features on the light bulb and the text simply said, “Our bulbs are burning hot, turn the lights off when you leave!”.
They compared how people would respond to the two posters by having each displayed in separate coffee rooms for two weeks. Although the coffee rooms were different, they were matched as closely as possible on as many parameters as possible (similar business, # of employees, et cet) such that this is a correlated groups design. Percent likelihood of someone turning off the light upon exiting was calculated every day and is presented below. Select and conduct the most appropriate statistical test based on the premise that all assumptions are met for a parametric test and this is a correlated groups design. Determine whether there is a difference in likelihood of turning off the light based on the poster campaign.
Anthropomorphism |
Nonanthropomorphism |
87.2 |
76.3 |
78.1 |
86.2 |
77.5 |
76.5 |
91.9 |
87.0 |
86.6 |
77.6 |
87.4 |
86.8 |
76.5 |
76.2 |
65.7 |
65.2 |
88.3 |
55.4 |
57.5 |
51.7 |
68.6 |
61.8 |
67.9 |
53.7 |
73.5 |
62.9 |
77.7 |
57.6 |
The SPSS output is:
The SPSS graph is:
The hypothesis being tested is:
H0: µd = 0
Ha: µd ≠ 0
The p-value is 0.012.
Since the p-value (0.012) is less than the significance level (0.05), we can reject the null hypothesis.
Therefore, we can conclude that there is a difference in the likelihood of turning off the light based on the poster campaign.
If the assumptions had been violated, the Wilcoxon Signed-Rank test would be the most appropriate statistical test.