In exercises that call for two-sample procedures, you may use either of the two approximations for the degrees of freedom that we have discussed: the value given by your software or the smaller of and . Be sure to state clearly which approximation you have used.

Question 7.52

7.52 Sadness and spending.

The “misery is not miserly” phenomenon refers to a sad person’s spending judgment going haywire. In a recent 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.26 Here are the data:

sadness

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
  1. Examine each group’s prices graphically. Is use of the procedures appropriate for these data? Carefully explain your answer.
  2. Make a table with the sample size, mean, and standard deviation for each of the two groups.
  3. State appropriate null and alternative hypotheses for comparing these two groups.
  4. Perform the significance test at the level, making sure to report the test statistic, degrees of freedom, and -value. What is your conclusion?
  5. Construct a 95% confidence interval for the mean difference in purchase price between the two groups.