### Guilt in Decision MakingThe effect of guilt on decision making was investigated in the January 2007 issue of the *Journal of Behavioral Decision Making*. A study of 77 volunteer students examined how different emotional states affect decision-making processes. Each participant was randomly assigned to one of three emotional states: guilt, anger, or neutral, through a reading/writing task.After the task, they faced a decision problem where the provided option had predominantly negative features (e.g., deciding whether to spend money repairing an old car). Before making a decision, participants were asked to list possible, more appealing alternatives.The researchers compared the average number of alternatives listed across the three emotional states using an analysis of variance (ANOVA) for a completely randomized design. Below is a partial ANOVA summary table:| Source | df | F-Value | p-Value ||-----------------|----|---------|---------|| Emotional State | 2 | 22.68 | 0.001 || Error | 74 | | || Total | 76 | | |**a. What conclusion can you draw from the ANOVA results?**The F-Value of 22.68 with a p-Value of 0.001 suggests that there is a statistically significant effect of emotional state on the number of alternatives listed. This indicates that the emotional state influences decision-making processes in this context. **b.** A multiple comparisons of means procedure was applied to the data using an experimentwise error rate of 0.05. Explain what the 0.05 represents.**c.** The multiple comparisons yielded the following results. What conclusion can you draw?| Sample mean | 1.90 | 2.17 | 4.75 ||--------------|------|------|------|| Emotional state | Angry | Neutral | Guilt |### Explanation- **Experimentwise Error Rate of 0.05:** This represents the probability of making at least one Type I error in a set of hypotheses tests. A Type I error occurs when a true null hypothesis is incorrectly rejected. The value 0.05 signifies a 5% risk of such errors.### Analysis of Results- **Sample mean for Angry:** 1.90- **Sample mean for Neutral:** 2.17- **Sample mean for Guilt:** 4.75### ConclusionThe differences in the sample means suggest that there is a noticeable variation among the emotional states, with "Guilt" having a substantially higher mean. This may indicate that participants experiencing guilt exhibit a distinct behavior or response level compared to those in angry or neutral states. Further statistical analysis could confirm whether these differences are statistically significant.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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3.86 Guilt in decision making. Refer to the Journal of Behavioral Decision Making (Jan. 2007) study of the ef- fect of guilt emotion on how a decision maker focuses on the problem, Exercise 3.59 (p. 142). The results (number responding in each category) for the 171 study participants are reproduced in the accompanying table. Suppose one of the 171 participants is selected at random. Choose Stated Option Emotional State Guilt 45 Anger 8 Neutral 7 Totals 60 Do Not Choose Stated Option Totals 1842 57 50 58 49 56 111 171 Based on Gangemi, A., and Mancini, F. "Guilt and focusing in decision-making." Journal of Behavioral Decision Making, Vol. 20, Jan. 2007 (Table 2). a. Given the respondent is assigned to the guilty state, what is the probability that the respondent chooses the stated option? b. If the respondent does not choose to repair the car, what is the probability of the respondent being in the anger state? c. Are the events {repair the car} and {guilty state} independent?
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Hypothesis Testing
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