answer in detail

In order to assess the effectiveness of a particular drug for blood pres- sure stabilisation, a multivariate random sample has been obtained from 30 patients. For each patient, the blood pressure measurements were taken across 14 consecutive days, and a blood pressure vector with 14 elements has been formed. For individual i, the blood pressure vector is denoted by Ti = (Ti,1, . .., Ti,14) . We assume that the observations are independent and each observation T, = (Ti,1, ..., Ti,14) comes from a multivariate normal dis- tribution N14(u, E), where u = (/1, . .., /14) and the covariance matrix E are unknown. The observations can be arranged in a matrix form as C1,14 X = . . C30.1 X30,14 We want to test the hypothesis Ho : /1 = /2 = .. . = /14, where it represents mean blood pressure on day t after taking the drug. (a) [3 marks] Explain why ANOVA is generally NOT appropriate for test- ing the hypothesis Ho (b) [4 marks] Clearly explain how to test Ho. In your answer, you need to include: assumptions made, test statistic and how do you decide to reject or retain the null hypothesis. Use a = 5% significance level. (c) [4 marks] Design a statistical test for testing the new null hypothesis Ho : /1 = au2 = au3 = ... = al3/14, where a is a known constant. In your answer you MUST specify clearly the test statistic, the distribu- tion of the test statistic and decision rule