Consider the situation described in Exercise 10-87.

(a) Redefine the parameters of interest to be the proportion of lenses that are unsatisfactory following tumble polishing with polishing fluids 1 or 2. Test the hypothesis that the two polishing solutions give different results using α = 0.01.

(b) Compare your answer in part (a) with that for Exercise 10-87. Explain why they are the same or different.

(c) You wish to use α = 0.01. Suppose that if p₁ = 0.9 and p₂ = 0.6, you wish to detect this with a high probability, say, at least 0.9. What sample sizes are required to meet this objective?

Exercise 10-87

Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble polished using the first polishing solution, and of this number, 253 had no polishing-induced defects. Another 300 lenses were tumble-polished using the second polishing solution, and 196 lenses were satisfactory upon completion.