3. A biologist was interested in the effect of different colours of light on the growth of bacteria. She had 40 lights with filters to allocate to various treatments. An equal amount of bacteria was placed on each of the 40 petri dishes and the dishes were randomly allocated using the following treatments. \\\\ 1:"White" or unfiltered light for 30 hours, \\ 2: Blue light for 30 hours, \\ 3: Green light for 30 hours, \\ 4: Blue light for 15 hours and Green light for 15 hours. \\ Let m, be the mean response for treatment i, for i = 1, 2, 3, 4. Consider the following linear combinations of the factor level means: Ing = 3/1 - 142 - 14 -PA- (a) Which of the three linear combinations of the factor level means are contrasts? Why? (b) Refer to part (a). Explain, in words, the meaning of each contrast. (c) What type of experiment is being implemented here? (d) Write down an appropriate ANOVA model for this experiment. (e) Suppose that we fitted a linear model with deviation coding to express the bacteria growth according to the light factor. Give the matrix & of the coefficients of the contrasts In , by, &, in terms of the coefficients of the model