Question 7.104

7.104 Two-sample test versus matched pairs test.

Consider the following data set. The data were actually collected in pairs, and each row represents a pair.

paired

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
  1. 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 statistic, degrees of freedom, and -value for the two-sided alternative.
  2. Now analyze the data in the proper way. Compute the sample mean and variance of the differences. Then compute the statistic, degrees of freedom, and -value.
  3. Describe the differences in the two test results.