You randomize 102 students in two groups in order to run an experiment. The first group has 64 students: their average age is 15.4 with a standard deviation of 2.1. The second group has 38 students: their average age is 13.8 with a standard deviation of 3.4. You want to test that the groups are balanced when it comes to their age: that is, that there is no statistical difference between the average age in the two groups.

1. What is the value of the estimator for the difference in average age between the first group and the second?

2. What is the value of the standard error of the estimate?

3. What is the value of the t-statistic?

4. What is the interval for the p-value?