[All Steps] Consider the following data set. The data were actually collected in pairs, and each row presents a pair. Suppose that we ignore the fact that
Question: Consider the following data set. The data were actually collected in pairs, and each row presents a pair.
- 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.
- 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.
- Describe the differences in the two results.
| Group 1 | Group 2 |
| 48.86 | 48.88 |
| 50.6 | 52.63 |
| 51.02 | 52.55 |
| 47.99 | 50.94 |
| 54.2 | 53.02 |
| 50.66 | 50.66 |
| 54.91 | 47.78 |
| 48.79 | 48.44 |
| 47.76 | 48.92 |
| 51.13 | 51.63 |
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