Suppose that we take a sample of n = 10 measurements from a normal distribution with 1.

Suppose that we take a sample of n = 10 measurements from a normal distribution with σ1. We wish to test H0: μ = 0 against H1: μ > 0. The normal test statistic is Zo = X/ (σ/√n), and we decide to use a critical region of 1.96 (that is, reject H0 if z0 > 1.96).
(a) What is a for this test?
(b) What is B or this test, if μ = 1?
(c) If a sign test is used, specify the critical region that gives an value consistent with B for the normal test.
(d) What is the value for the sign test, if μ = 1? Compare this with the result obtained in part (b).