Question: It has been suggested that treatment 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 castings were made from a single formulation of the plastic and seven casting were randomly assigned to each of the treatment groups. “Wear” was determined by measuring the increase in haze after 200 cycles of abrasion.

(a) Is there evidence of a difference in mean wear among the four treatments? Use \(\alpha =0.05\). Can you reject the null hypothesis?

(b) Estimate the mean difference in haze increase between treatments B and C using a 99% confidence interval. Is there a discernible difference?

(c) Find a 90% confidence interval for the mean wear for lenses receiving treatment A. If it is believed that \({{\mu }_{A}}=8.75\) for treatment A, based on your interval can you accept this claim.