Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing i
ntraocular lenses used in the human eye following cataract surgery. 300 lenses were tumble-polished using the first polishing solution, and of this number, 252 had no polishing-induced defects. Another 300 lenses were tumble-polished using the second polishing solution, and 195 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).
1 answer:
Answer:
p-value: 1.000
There is enough evidence at the 1% level of significance to suggest that the proportions are not equal.
Step-by-step explanation:
We will be conducting a difference of 2 proportions hypothesis test
The hypothesis for this test is:
H_0: p1 - p2=0
H_a: 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
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