7.61 When is 30/31 days not equal to a month? Time can be expressed on different levels of scale; days, weeks, months, and years. Can the scale provided influence perception of time? For example, if you placed an order over the phone, would it make a difference if you were told the package would arrive in four weeks or one month? To investigate this, two researchers asked a group of 267 college students to imagine their car needed major repairs and would have to stay at the shop. Depending on the group he or she was randomized to, the student was either told it would take one month or 30/31 days. Each student was then asked to give best- and worst-case estimates of when the car would be ready. The interval between these two estimates (in days) was the response. Here are the results:30
| Group | n | s | |
|---|---|---|---|
| 30/31 days | 177 | 20.4 | 14.3 |
| One month | 90 | 24.8 | 13.9 |
(a) Given that the interval cannot be less than 0, the distributions are likely skewed. Comment on the appropriateness of using the t procedures.
456
(b) Test that the average interval is the same for the two groups using the significance level. Report the test statistic, the degrees of freedom, and the P-value. Give a short summary of your conclusion.