<s>[INST] We have a sample of size 100 from a normal population with unknown mean and known variance \(\sigma^2=100\), and we want to test if the mean \(\mu\) is equal to 50 as claimed, against the alternative hypothesis that the mean is not equal to 50. The sample mean \(\overline{x}= 55\) and the sample standard deviation \(s=12\). We will use significance level \(\alpha=0.01\). Please calculate the test statistic \(T\) and state the rejection region.[/INST]