note: Answer cNote: Answer can ve provuded in writtrn form converted into pdf also.

Question 3 (9 Marks): use of a software is not recom- mended The multivariate observations of 4 variables were obtained for 20 subjects and these observations were denoted by X1, . .., T20, where each ; is a 4 x 1 vector containing 4 values from the 4 variables. Let the population mean vector be u = (M1, M2, M3, MA) . Suppose we wish to test the following hypotheses involving different contrasts: Let the significance level for the test be a = 5%. (a) (3 Marks) Explain how to test this hypothesis. In your answer you must include: (i) assumptions made, (ii) test statistic, and (iii) how to decide on rejecting or retaining the null hypothesis. (b) (3 Marks) Write down the T2 simultaneous confidence intervals for all contrasts. 2 (c) (3 Marks) Write down the Bonferroni simultaneous confidence intervals for all contrasts