3. (15%) Suppose that a random sample $X_1, \ldots, X_n$ is drawn from a normal distribution for which the value of the mean $\mu$ is unknown and the standard deviation is 2, and the following simple hypotheses are to be tested: $$H_0: \mu = -1$$ $$H_1: \mu = 1$$ Determine the minimum value of $\alpha + \beta$ (type I error+ type II error) that can be attained for each of following values of the sample size n: a. n=1 b. n=16