Blood tests are required by health department legislation to be reproducible across different pathology laboratories. Concern about the reliability of data from one pathology lab led to a study In which blood semm samples were divided and sent to two laboratories for testing. One'half of each sample was sent to the CSI. Laboratory {Lab 1] and the other sent to the Astra Zeneca laboratory [Lab 2]. Measurements of specic antibodies {th and levels of T cells le} were obtained. forn = 11 sample splits, from the two laboratories. m-IEZI-ME WEE-Emma l-Iere &= 31 = za.os s =[1?93.29 tears 5-1: 0.00062 o.cocl $2 313.32 ' ' 194.13 3767.56 ' ' o.oools oncozs' Eigenvalues and eigenvectors of 5,. are: 11 = 4.047.759; = [0.33.034] A; = 1513.10.2i = [0.94.o.33]. 3] Using the information above construct and sketch a joint 95% condence region [ellipse] for the mean difference vector 5" using the data and results above. Show all your formula and working {4 marks] b} We are interested in whether the point, 6* = [61.62] = [0.01. falls outside the 95% contourfellipse. Does it? Justify your answer. [2 marks] c} At what point in two-dimensional space is the ellipse centred? (1 mark] d] Determine the half length of the major axis. {2 marks] e] Determine the half length of the minor axis. [2 marks] f] In which direction does the major axis lie? {2 marks} g] In which direction does the minor axis lie? [2 marks] h] Using the information above also construct the Bonferrcni 95% simultaneous intervals for the components of the mean difference vector 6'. [4 marks] i] Out of the 11 samples tested across the 2 laboratories can you detect any outlier samples? {1 mark] Critical t values (you choose the correct one}: mono] = 1.372 more] = 1.312 moms] = 2.262 tMDJJI25} = 2.634 tDDI] = 2.763 moms} = 3.16 Critical F values (you choose the correct one]: sumac] = 3.01 woos] = 4.25 sermon = soc