You have run a study evaluating 4 variations of a motivational treatment (A, B, C, and D). The 5th treatment is a control treatment. Fifty (50) undergraduate seniors were recruited for the study and randomly assigned to one of the five treatments. The study was balanced, so there were 10 students per treatment. The response is a measure of productivity. The data are in motivate.csv. Assume a pooled error variance for all the parts where that is relevant. a) Use 1-way ANOVA to test the hypothesis that the five treatments have the same mean productivity. Report the test statistic, p-value, and a one-sentence interpretation / conclusion.

b) The structure of the five treatments strongly suggests using a linear contrast that compares the control to the average of the four other treatments (A, B, C, and D). What are the coefficients for this contrast? Your answer will be a list of the five treatments with their associated coefficients. c) Estimate the value of the contrast in part b and its standard error. Note: Check the order of the treatments used by your program. Make sure you enter coefficients into the computer in the appropriate order. d) Test the hypothesis that the true value of the contrast in part b = 0. Report your p-value and a one-sentence interpretation / conclusion. e) The investigators are also interested in the difference between treatments C and D. What are the coefficients for this contrast? Your answer will be a list of the five treatments with their associated coefficients. f) Are the two contrasts (from parts b and e) orthogonal? Why or why not?

treatment	productivity
control	44
control	24.5
control	9.3
control	23.3
control	21
control	53.5
control	30.2
control	76.6
control	8.3
control	29.3
A	31.2
A	54.9
A	50.1
A	48.3
A	46.6
A	55.8
A	44.6
A	57.5
A	49.5
A	47.4
B	56.1
B	50.6
B	34
B	22
B	49
B	58.7
B	63.7
B	33.7
B	35.7
B	49.5
C	37.7
C	47.1
C	55.1
C	83.2
C	70.4
C	31.9
C	42.4
C	50.4
C	56.2
C	36.1
D	56.6
D	52.2
D	29.5
D	63.2
D	40.4
D	43.7
D	59.9
D	27
D	42.5
D	45.7