EXAMPLE 7.16
Timing of food intake. In the setting of Example 7.15, let’s consider a much smaller study that collects weight loss data from only five participants in each eating group. Also, given the results of this past example, we choose the one-sided alternative. The data are
| Group | Weight loss (kg) | ||||
|---|---|---|---|---|---|
| Early eater | 6.3 | 15.1 | 9.4 | 16.8 | 10.2 |
| Late eater | 7.8 | 0.2 | 1.5 | 11.5 | 4.6 |
First, examine the distributions with a back-to-back stemplot (the data are rounded to the nearest integer).
| Early | Late | |
|---|---|---|
| 0 | 02 | |
| 96 | 0 | 58 |
| 0 | 1 | 2 |
| 75 | 1 |
While there is variation among weight losses within each group, there is also a noticeable separation. The early-eaters group contains four of the five largest losses, and the late-eaters group contains four of the five smallest losses. A significance test can confirm whether this pattern can arise just by chance or if the early-eaters group has a higher mean. We test
H0: μ1 = μ2
Ha: μ1 >μ2
The average weight loss is higher in the early-eater group (t = 2.28, df = 7.96, P = 0.0262). The difference in sample means is 6.44 kg.