The output voltage of a power supply unit has an unknowndistribution. Using a sample size of 36, sixteen samples are takenwith the following sample-mean values: 10.35 V, 9.30 V, 10.00 V,9.96 V, 11.65 V, 12.00 V, 11.25 V, 9.58 V, 11.54 V, 9.95 V, 10.28V, 8.37 V, 10.44 V, 9.25 V 9.38 V and 10.85 V. Let µ and?2 denote the mean and the variance of theoutput voltage of the power supply unit. (a) What distributiondescribes the sample-mean? What are the parameters of thedistribution (in terms of µ and ?2 )?(b) Test the hypothesis that the population variance?2 = 36 V2 at 95% confidence. (c)Construct a two-sided 95% confidence interval for the population’sstandard deviation.
