7.67 Sadness and spending. The “misery is not miserly” phenomenon refers to a person’s spending judgment going haywire when the person is sad. In a study, 31 young adults were given $10 and randomly assigned to either a sad or a neutral group. The participants in the sad group watched a video about the death of a boy’s mentor (from The Champ), and those in the neutral group watched a video on the Great Barrier Reef. After the video, each participant was offered the chance to trade $0.50 increments of the $10 for an insulated water bottle.33 Here are the data:
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| Group | Purchase price ($) | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Neutral | 0.00 | 2.00 | 0.00 | 1.00 | 0.50 | 0.00 | 0.50 | ||
| 2.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | |||
| Sad | 3.00 | 4.00 | 0.50 | 1.00 | 2.50 | 2.00 | 1.50 | 0.00 | 1.00 |
| 1.50 | 1.50 | 2.50 | 4.00 | 3.00 | 3.50 | 1.00 | 3.50 | ||
(a) Examine each group’s prices graphically. Is use of the t procedures appropriate for these data? Carefully explain your answer.
(b) Make a table with the sample size, mean, and standard deviation for each of the two groups.
(c) State appropriate null and alternative hypotheses for comparing these two groups.
(d) Perform the significance test at the level, making sure to report the test statistic, degrees of freedom, and P-value. What is your conclusion?
(e) Construct a 95% confidence interval for the mean difference in purchase price between the two groups.