Refer to Exercise 15.71. The data in this table are the cadmium concentrations found in aphids that fed on the plants grown in soil amended with sludge.

a. Use the diagnostic plots to assess whether the assumptions of normality and constant variance are reasonable in this case.
b. Based on your conclusions in part a, use an appropriate statistical method to test for significant differences in cadmium concentrations for the six rates of application.

Exercise 15.71
An experiment was performed to determine whether there is an accumulation of heavy metals in plants that were grown in soils amended with sludge and whether there is an accumulation of heavy metals in insects feeding on those plants.8 The data in the table are cadmium concentrations (in g/kg) in plants grown under six different rates of application of sludge for three different harvests. The rates of application are the treatments. The three harvests represent time blocks in the two way design.

a. Based on the diagnostic plots, are you willing to assume that the normality and constant variance assumptions are satisfied?
b. Using an appropriate method of analysis, analyze the data to determine whether there are significant differences among the responses due to rates of application.

Harvest Rate Control 16.2 16.9 12.7 31.3 38.5 20.6 55.8 119.4 65.8 181.1 184.6 196.4 163.7 242.8 128.4 182.0 191.3 Residuals versas Rate (nsponse is cadmian 15 Rate Normal Probability Plet of the Residuabs ponse is cadmiumi 50 25 50 Residual Harvest Rate Conto 1621 57 200.4 278.2 220.0 2107 294.8 1944 79.0 341.1 204.3 203.7 330.2 344.2 199.8 199.6 218.9 236.1 Residuals versus Rate (response is cadmium) 10 10 -20- 30 Rale Normal Probability Plot of the Residuals (rusponse is cadmium) 95 90 80 70 40 30 -40 -30 2000 0 20 30 44 50 Residual