Exercise 15. For the following four cases, perform statistical tests with significance level a = 5%, testing the hypothesis Ho : u = 0 against the alternative H1 : u + 0. Show how you perform each test and state the outcome. a) We have observed 100 independent, normally distributed values with known variance o2 = 1. The average of the observed values is -0.18. b) We have observed 10 independent samples of a normal distribution with known variance 02 = 4: The observed values are 0.595, 3.923, 0.12, 1.078, 0.578, 1.575, 2.26, -0.031, 1.733, and 1.135. c) We have observed 10 independent samples from a normal distribution. The sample mean is a = -1.405, the exact variance is unknown but the sample variance is s = 1.456