Question 1 [19 marks] A lecturer of a Chinese to English translation unit at a university was interested in comparing the difculty level of four passages (A-D] of text in Chinese. Firstly she selected twe nty-four students who obtained a similar mark in their rst Chinese to English translation assignment. The 24 students were then randomly assigned to translate one of those four passages, having six [6] students in each passage group. All 24 students were then given 30 minutes to complete the translation task in a class. After that, their scripts (completed assignments] were collected and marked out of 40 marks. The data obtained is shown below and also stored in Excel file, marksbypassage.xlsx, available on iLearn. You may use R for some parts of this question. Passage A B c D 22 21 27.5 16.5 32 22.5 20 13.5 29 17.5 23 19 25 25 20 20 31 23 33 25 32.5 26 32 21 .5 a] Explain what design is used here. b} Carry out an analysis of variance using the data given and show the resulting ANOVA table. Note: You must illustrate how SST, SSE and SSTotal in this ANOVA table are calculated by hand. c] Check and comment on model assumptions for the ANOVA above. d] Based on the results in the ANOUA table obtained above, test if there is any difference in the level of difficulty for translation across the four passages at the 5% significance level. e] If one wishes to compare all pair-wise passage means simultaneously, explain which multiple pair- wise comparison method or procedure is preferred for the data here. What is its associated critical value at an overall 5% significance level? Question 1 {Contd.] f} Suppose passages A and C were selected from some recent Chinese literature but passages B and D are from a Chinese novel published more than twenty years ago. It would be interesting to compare passages A and C with passages B and D. It is also of interest to compare passage A with passage C, as well as passage B with passage D. Write down the three corresponding contrasts. Check and explain if these three contrasts form a full orthogonal contrast set for this experi mentfstu dy. (Note: Let's code 1 for passage A, 2 for B, 3 for C and 4 for D.) g] What is the preferred test or method for investigating the three contrasts above simultaneously? Why