Question

Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing intraocular lenses used in the human eye following cataract surgery. 300 lenses were tumble-polished using the first polishing solution, and of this number, 249 had no polishing-induced defects. Another 300 lenses were tumble-polished using the second polishing solution, and 196 lenses were satisfactory upon completion. Is there any reason to believe that the two polishing solutions differ? Use α = 0.01. What is the P-value for this test? There significant difference in the proportion of polishing-induced defects produced by the two polishing solutions at the 0.01 level of significance. The P-value is . Round your answer to three decimal places (e.g. 98.765).

Answer 1

p-value: 1.000

There is enough evidence at the 1% level of significance to suggest that the proportions are not equal.

Explanation:

We will be conducting a difference of 2 proportions hypothesis test

The hypothesis for this test is:

H0: p1 - p2=0

Ha: p1 - p2 ≠0

(p1 ) = 252/300 = 0.84

(p2) = 195/300 = 0.65

This is a 2 tailed test with a significance level of 1%. So our critical values are: z > 2.575 and z < -2.575

See the attached photo for the calculations for this test