Consider the following Z-test. Suppose the population distribution is N(, ) with a known . We test: H0 : = 0 vs Ha : = 1 > 0 at significance level , where 0, 1 are known values. Sample size = n.

If we only increase 1 without changing any other setting of the original problem, then: the critical value of X will change how? and the type I error rate of the test will change how?

and the power of the test will change how?