Question

The diameter of steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes n1 = 15 and n2 = 17 are selected, and the sample means and sample variances are 8.73 and 0.35 respectively for sample 1 and 8.68 and 0.40 respectively for sample 2. Find the lower bound of a 95% two-sided Cl on 01/02 Use at least two decimal digits

Answer 1

n 2017 Given that two random samples of sizes n = 15 and Sample means are, X = 8.73 X2 = 8.68 Sample variances are; 5,2- 0,35, S2=0.40 2 . g 5% two sides confidence interval for 0/02 is, Р si 5,2 0.95 2 2 b s Sz oz Sa 1-dcogs ... d = 0,os we find values a and b such that I-a/2 P [ Fear t), chy-17 29] :: P/F14,11 > a -0,975 a= 0.34 20 >6 de b] P[Ferit, chat) P[F14517 > b 0,025 i', b = 2.8170 .. Lower bound - 7 si s b 0.35 V 2,8170 X 0.40 no 0.3106 0,5573