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5. A random sample of size 12 was taken from a normal population in order to estimate the mean u of the population. The 12 observations were: 163 228 170 200 191 140 215 234 197 185 173 206 for which Ex = 2302 and _ 12 = 449914. (a) Calculate a 99% equal-tailed confidence interval for the mean p. (b) Test Ho : # = 200 v H1 : u # 200 at the 1% level of significance by using an appropriate test statistic and critical region. State clearly the conclusion and relate your answer to the confidence interval found in (a). [5] (c) Calculate the p-value of the observed test statistic in (b) and give its interpreta- tion