7.126 Two-sample t test versus matched pairs t test. Consider the following data set. The data were actually collected in pairs, and each row represents a pair.
| Group 1 | Group 2 |
|---|---|
| 48.86 | 48.88 |
| 50.60 | 52.63 |
| 51.02 | 52.55 |
| 47.99 | 50.94 |
| 54.20 | 53.02 |
| 50.66 | 50.66 |
| 45.91 | 47.78 |
| 48.79 | 48.44 |
| 47.76 | 48.92 |
| 51.13 | 51.63 |
(a) Suppose that we ignore the fact that the data were collected in pairs and mistakenly treat this as a two-sample problem. Compute the sample mean and variance for each group. Then compute the two-sample t statistic, degrees of freedom, and P-value for the two-sided alternative.
(b) Now analyze the data in the proper way. Compute the sample mean and variance of the differences. Then compute the t statistic, degrees of freedom, and P-value.
(c) Describe the differences in the two test results.