It has been hypothesized that treatments (after casting) of a plastic used in optic lenses will improve wear. Four different treatments are to be tested. To determine whether any differences in mean wear exist among treatments, 28 casting from a single formulation of the plastic were made and 7 castings were randomly assigned to each of the treatments. Wear was determined by measuring the increase in “haze” after 200 cycles of abrasion (better wear being indicated by smaller increases). The data collected are reported in the accompanying table.     Treatment A B C D 9.16 11.95 11.47 11.35 13.29 15.15 9.54 8.73 12.07 14.75 11.26 10 11.97 14.79 13.66 9.75 13.31 15.48 11.18 11.71 12.32 13.47 15.03 12.45 11.78 13.06 14.86 12.38 Q. Construct ANOVA table. At the 5%, is there evidence of significant difference in mean wear among the four treatments? Determine which treatments differ in average wear.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...