Question

(20.4057 47.52475247 380, D2-3026 2) We have productivity data from 2 mills Data from Mill 1:10.17,21,22,22,23,27,28,29,32,37,38,40, 13, 346, 22-10118 Data from Mill 2: 14,14,15,15,15,18,18,18,19,19,19,20,22,22,23,23,26,29,31, -19, A Calculate the mean and standard deviation for mill 1 B. Calculate the mean and standard deviation for mill 2 C Assume the two are normal distributions, and the standard deviations are correct for the two populations the mills are drawn from. Finally assume the population mean for the two distributions are the same Use the variance rules to cakulate the variance of the difference of the means b. Calculate the score for the difference of the means. c. Determine the probability of seeing that Z score or one with a larger absolute value.

Answer 1

Given:

Data for mill 1 is

n = 13

$\sum$x = 346

$\sum$x² = 10118

Data for mill 2

n = 19

$\sum$x = 380

$\sum$x² = 8026

A>for milli # mean, x= Ex = 346 = 26.61 13 .Mean, ã = 26.61. + Standard deviation :- SD- ECX;-)2 - -Ex-navo =jig-TX10118 - 18.-1X(2661)2 = 76.06 = 8.72 .:50=18.72] By Meanit = {x=380 = 20 a=20] Standard deviation:- so-1g-TX8026-19_,x(2012 - 523.67 = 4.86 .:50=14686] 19

& Assume the two are normal distribution and the standard deviation are correct for the two population the mells are drawn from. Assume the population mean for the two distribution are 'same. let XINN(M, 76.06) X2 N Nalli 23.67) Cehere el is common mean. ay The variance of the difference of mean v (81-82) = V(XI) + U(72) - ($0?+(50) 76.0 67 19 = 76.96 +23.67 = 7.096 ::0 (X-R2) = 7.096) od z=21-52_-26.61-20 -2.48 Juc ,-72) 12=2.48) 17.096 = 2

c) 2P(z>2.48) = 2[1-P(z<2.48) 2[1-0.9934] = 0.0132