### 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

Section: Chapter Questions

Problem 1P

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4.78 GUILT IN DECISION MAKING. The Journal of Behavioral Decision Making (January 2007) published a study of how guilty feelings impact on-the-job decisions. In one experiment, 57 participants were assigned to a guilty state through a reading/writing task. Immediately after the task, the participants were presented with a decision problem where the stated option had predominantly negative features (e.g., spending money on repairing a very old car). Of these 57 participants, 45 chose the stated option. Suppose 10 of the 57 guilty-state participants are selected at random. Define x as the number in the sample of 10 who chose the stated option. a. Find P(x = 5). b. Find P(x = 8). c. What is the expected value (mean) of x?
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Hypothesis Testing
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