A physicist made 20 measurements of the temperature of an object and obtained sample standard deviation of 1.1. He knew that his thermometer had a measurement error which is normally distributed with zero mean. Physicist wants to test a hypothesis that

A physicist made 20 measurements of the temperature of an object and obtained sample standard deviation of 1.1. He knew that his thermometer had a measurement error which is normally distributed with zero mean. Physicist wants to test a hypothesis that measurement error has variance 1. (a) Test null hypothesis at $10 \%$ significance level. (b) Find power of the test when true variance of measurement error $\sigma^{2}=1.3$ (use CHISQ.DIST function in Excel or scipy.stats.chi2.cdf function in Python). (c) How your test of variance $\sigma^{2}$ would change if you know that true temperature is $60^{\circ}$ and $\widehat{\sigma^{2}}=1.25$ where $\widehat{\sigma^{2}}=\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2} ?$