With reference to Exercise 10.55, find a large sample 95% confidence interval for the true difference of probabilities.

Data From Exercise 10.55

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10.55 As a check on the quality of eye glasses purchased over the internet, glasses were individually ordered from several different online vendors. Among the 92 lenses with antireflection coating, 61 prescriptions required a thickness at the center greater than 1.9 mm and 31 were thinner. Of the 61 thicker lenses, 12 failed im- pact testing while 18 of the 31 thinner lens failed.