Question

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. a) Generate a 95% confidence interval for the difference between the proportion of satisfactory lenses using the first solution and the proportion using the second solution. [Select) b) Interpret this interval. (Select ]

Answer 1

Answers & Given information, no.dor polishing indueed de feets in first solution, X, = 253 number Lenses were satisfactory cupon completion, X 2 = 196. nord lenses were farkle gokshed using frost solution, - 500 numberd lenses were tremble using and soketion, ng= 300. coeficience level, e =0.45 derd of significance , d = 10 . 1-095 = 0.05 Now, first Sampler pzoponition, me aning 5300 0.843 and sampler proportion, Pe = sehen = 1900 = 0.653

Now, find o 95% confidence interval for the difference in two population proportion : (P1-1)-261-*x) ,600.) * 0-727-has C.F. J+2 6+Way 14 (172) + . 2017] 12 Here a critical is, ze = za = 70.05 = 1.98. Coving fromial cekecekatan) Now) 994. confidence nervat is, C+i. 3-363)* ) Ex (-1); RX (:2) 4.-RS CP-Re)t =(1-* * * * * (-7.), FACENTER

-> (0.843–0.653 )– 1.96 x H 1.0.843*(1-01843), 0.6537(1-06 Ve 300 300 0.843--0.653 )+1.96 X 1,0.843% (-0,843) V 300 / at 0.6538U-0.653) 300 ---> 0,19-196% (4.4117x164+ 7.553033333 X104) Pi-Pas (0-10) 4196 x y Gy. una x16" x 4.5-203283 Nit") -> (0.19 ) 1968 (0.3459007565) Pi-Pes Co.19) +1.96% (0.5459007565) --> (0,19)-0.06783 P1-83 < Co.193+00678 -> 0.1239,-P230.26 Som :: 94.4. confidence interveel is, - 0.125.P. -P2 3.0.26. y This conficina internal shows that we are 95%. Confident that the difference in the two population proportion is lies within that interral & there is 5% chance that it is falls outside this intervalo b