Question: A research team takes a sample of 8 observations from the random variable Y, which has a normal distribution \[N(\mu ,{{\sigma }^{2}})\]. They observe \[{{\bar{y}}_{8}}=537.2\], where \[{{\bar{y}}_{8}}\] is the average of the eight sampled observations and \[{{s}^{2}}=953.2\] is the observed value of the unbiased estimate of \[{{\sigma }^{2}}\], based on the sample values. Test the null hypothesis that \[{{H}_{0}}:\ {{\sigma }^{2}}=169\] against the alternative \[{{H}_{1}}:\ {{\sigma }^{2}}\ne 169\] at the 0.10, 0.05, and 0.01 levels of significance.