Consider the following data set. The data were actually collected in pairs, and each row repress 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 t a two-sample problem. Compute the sample mean and variance for each group. Then c two-sample t statistic, degrees of freedom (conservative one), and p-value for the two-sided (4 pts) b) Redo a) using R and attach the output. (use the exact df) (4 pts) c) Now analyze the data in the proper way. Compute the sample mean and variance of the Then compute the t statistic, degrees of freedom, and p-value for the two-sided alternative d) Redo c) using R and attach the output. (4 pts)