Question: Assuming that the following sample of 10 numbers arise from a Normal distribution with mean and standard deviation \(\sigma \) = 5.7, obtain, from first principles, 95% and 99% confidence intervals for \(\mu \)

39.1 22.2 37.3 26.9 24.7 28.9 28.4 30.6 28.2 22.4

Evaluate a test statistic for the null hypothesis Ho: \(\mu \) = 30 against the two-sided alternative hypothesis H₁: \(\mu \) \(\ne \) 30, and by plotting this on its reference distribution, identify and calculate the corresponding p-value associated with Ho. What are your conclusions about Ho?