Question

The output voltage of a power supply unit has an unknown distribution. Using a sample size of 36, sixteen samples are taken with 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, 10.28 V, 8.37 V, 10.44 V, 9.25 V 9.38 V and 10.85 V. Let µ and σ² denote the mean and the variance of the output voltage of the power supply unit. (a) What distribution describes the sample-mean? What are the parameters of the distribution (in terms of µ and σ² )? (b) Test the hypothesis that the population variance σ² = 36 V² at 95% confidence. (c) Construct a two-sided 95% confidence interval for the population’s standard deviation.

Answer 1

I have used R. On R.H.S. is output and on L.H.S. is R code