Revisiting the sadness and spending study. In given Exercise, the purchase prices of a water bottle were compared using the two-sample t procedures that do not assume equal standard deviations. Compare the means using a significance test and find the 95% confidence interval for the difference using the pooled methods. How do the results compare with those you obtained in Exercise 7.49?
Exercise
Sadness and spending. The "misery is not miserly" phenomenon refers to how sadness affects a person's spending judgment. 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 film 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. Here are the data as follows:
(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 α = 0.05 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.