Let y0,y1, . . . ,yn be independent N , 2 random variables and compute y, and s2 from observations 1 through

Let y0,y1, . . . ,yn be independent N



μ ,σ 2

random variables and compute ¯ y·, and s2 from observations 1 through n. Show that (y0 − ¯ y·)/



σ 2+σ 2/n ∼ N(0,1) using results from Chapter 1 and the fact that linear combinations of independent normals are normal. Recalling that y0, ¯y·, and s2 are independent and that (n−1)s2/σ 2 ∼ χ 2(n−1), use Definition 2.1.3 to show that (y− ¯ y·)/



s2 +s2/n ∼ t(n−1).

Table 2.4: Observations on the charge of an electron.

4.781 4.764 4.777 4.809 4.761 4.769 4.795 4.776 4.765 4.790 4.792 4.806 4.769 4.771 4.785 4.779 4.758 4.779 4.792 4.789 4.805 4.788 4.764 4.785 4.779 4.772 4.768 4.772 4.810 4.790 4.775 4.789 4.801 4.791 4.799 4.777 4.772 4.764 4.785 4.788 4.779 4.749 4.791 4.774 4.783 4.783 4.797 4.781 4.782 4.778 4.808 4.740 4.790 4.767 4.791 4.771 4.775 4.747