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.