An article in Quality Engineering ["Estimating Sources of Variation: A Case Study from Polyurethane Product Research" (1999-2000, Vol. 12, pp. 89-96)] studied the effects of additives on final polymer properties. In this case, polyurethane additives were referred to as cross-linkers. The average domain spacing was the measurement of the polymer property. The data are as follows:

Cross-Linker Level Domain Spacing (nm -1 8.2 8.0 8.2 7.9 8.1 8.0 -0.75 8.3 8.4 8.3 8.2 8.3 8.1 -0.5 8.9 8.7 8.9 8.4 8.3 8.5 0 8.5 8.7 8.7 8.7 8.8 8.8 0.5 8.8 9.1 9.0 8.7 8.9 8.5 1 8.6 8.5 8.6 8.7 8.8 8.8 Is there a difference in the cross-linker level? Perform an ANOVA using a = 0.05. Find the P-value of the test. Estimate the variability due to random error