Question

in a chemical process two catalysts are being compared for their effect on the output of the process reaction. a sample of 15 batches with catalyst A gave an average yield of 436 with sample standard deviation 4. the 17 batches with catalysts B gave an average yield of 422 with sample variance 25. find 99% confidence interval for the difference between the population means assuming the populations are approximately normally distributed with equal variances

Answer 1

Giuen the n, =t5 Answer a 2422 8, -4 S = 25 1-25 = ( 436 - 422) Cl-<) 100 7, < 99% The poded etimate spe the Comwon looionle o? is shown below ,? Cn -1)s,?+(^_-1)s" Sp (15-1)(4)"+(17-1)(2s 7-tl+SI (14X16) +( 16 X625) 30 224+1000 30 1224 30 2 40.8 = 6. 387

The E -y ae the meame d independent random Sampler of sized n and ^_ respectivly trom ay rovimate normal poqulation worth unknown but eqcal variancel a loo (1-«)1. conkidere ntorel for H, wly Is (I,-xI)- spd ulhere Sp is the pooled estimate of the population standard deuiation tale 1s the t- value d freedom degree v =n,+the -2 of dle leauing an area uring 50. I table value that toos - 17.25 V =1, + ng -2 ? - 15 +17 -2 2 30

A 94. Conkidence intaval for the defferene betion, the popuetation meand 381). 24-Cto725)(6.381) 15 1:7 (6.387 15 24 -B.344 c[H,~He]4 to.344 2 3.656 < (4,-dly)<4:344 (3.656,4.344 Conti dence Futer val hevee 9q Y.