Hi i need help with this question,

Question 1

A study was carried out to compare four different weight-reduction programs (1-4). Twenty-four overweight people were chosen for the study and each was then randomly assigned to take one of the four programs for one year (ie, having six people in each program). Data obtained is given below (negative and positive values indicate weight losses and gains respectively).

(Note: May use Minitab for any part below only if possible.)

Program

1 -59 22 -29 10 -23 72

2 -7 25 7 -8 40 64

3 -21 -54 -1 -44 -22 79

4 -27 -2 -77 -46 -11 93

1. a)Explain what design is used here.
2. b)Examine the data graphically and comment.
3. c)Carry out an analysis of variance using the data given, and illustrate how SST and SSE in the
4. resulting ANOVA table are computed.
5. d)Check and comment on model assumptions.
6. e)Based on the results in the ANOVA table obtained, test if there is any difference in mean weight
7. loss/gain across the four programs at the 5% significance level. Interpret the results.
8. f)Only if necessary and appropriate, carry out Tukey's simultaneous tests or compute Tukey's
9. simultaneous confidence intervals to compare all pair-wise program means. Comment.
10. g)Suppose that this study was initially planned to compare weight-reduction Program 3 with
11. Program 4, as well as Program 2 with the other three programs. Write down the two corresponding contrasts. Show if the two contrasts are orthogonal to each other, and suggest an appropriate method (test) to test simultaneously whether each of the two contrasts differs from zero.
12. h)Based on the graph from part b, suggest and write down one more contrast of interest, and show if this contrast together with the two contrasts above form a full orthogonal contrast set for this experiment/study.
13. i)Which test/method will you consider to investigate the three contrasts simultaneously? Why?