Question: Let T be a t-statistic for H0 : 0 versus H1 : 6 0. Since jT j!d jZj under H0, someone suggests

Let T be a t-statistic for H0 : µ Æ 0 versus H1 : µ 6Æ 0. Since jT j!d jZj under H0, someone suggests the test “Reject H0 if jT j Ç c1 or jT j È c2, where c1 is the ®/2 quantile of jZj and c2 is the 1¡®/2 quantile of jZj.

(a) Show that the asymptotic size of the test is ®.

(b) Is this a good test of H0 versus H1? Why or why not?

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