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).

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:

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

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

answer: i dont know i want points

step-by-step explanation: