Module 11a Activity - Independent Samples t-test
[Refer to Module 11b Slides for a practice example]
Good Smells and Business (Note: The calculations are done for you. This problem only requires a table look up and an explanation of the finding)
A restaurant compares the length (in minutes) of customer stays on a day when the scent of lavender was present (a relaxing smell) to a day when the scent of lemon was present (a stimulating smell).
Theorizing that a relaxing smell will cause customers to stay longer, the study works from the following hypothesis:
Null: The average stay on lavender days is equal to the average stay on lemon days.
Alternative: The average stay on lavender days is greater than the average stay on lemon days. (One-sided hypothesis)
The study randomly collects the total time for 30 customers on the lavender day (Sample 1) and 28 customers on the lemon day (Sample 2).
The average stay from the lavender day sample is 91.3 minutes and the average stay from the lemon day sample is 89.8 minutes.
Below is the equation for the t-test and the results from Excel data analysis software.
| t-Test: Two-Sample Assuming Unequal Variances | ||
| Lavender Days | Lemon Days | |
| Mean (minutes) | 91.3 | 89.8 |
| Variance | 222.9 | 238.3 |
| Observations | 30 | 28 |
| t Stat | 0.37 | |
1. Based on the rule of thumb, we use n-1 from the smaller sample for our degrees of freedom. What is the t-critical value for alpha=.05 to test our hypothesis (the t-table is pasted below).
2. Compare the critical value to the t-statistic. Can we reject the null hypothesis? Why or why not?
