Question: A research team takes a sample of 10 observations from the random variable Y, which has a normal distribution \[N(\mu ,{{\sigma }^{2}})\]. They observe \[{{\bar{y}}_{10}}=34.2\], where \[{{\bar{y}}_{10}}\] is the average of the ten sampled observations, and \[{{s}^{2}}=275.2\], where \[{{s}^{2}}\] is the observed value of the unbiased estimate of \[{{\sigma }^{2}}\], based on the sample values. Test the null hypothesis that \[{{H}_{0}}:\ {{\sigma }^{2}}=225\] against the alternative \[{{H}_{1}}:\ {{\sigma }^{2}}>225\] at the 0.01 level of significance. What is the 95% confidence interval for \[{{\sigma }^{2}}\] ? Note that an examination question would either ask for the test or the confidence interval.