The output of a power supply is assumed to be normally distributed. 16 observations taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38 and 10.85. (a) Test the hypothesis that the mean voltage equals 12V against a two-sided alternative using α=0.05. (b)Construct a 95% confidence interval on µ. (c) Test the hypothesis that σ2 =1 using α=0.05. (d)Construct a 95% two-sided confidence interval on σ. (e) Construct a 95% upper confidences interval on σ.