Question

A company that does manufacturing work has one facility that is automated and one that has manual functions. In order to estimate the difference in mean time it takes to complete a part on the two lines, the company has requested that a random sample of 16 parts at each facility be tracked from start to finish and the time required be recorded. The sample data to the right were recorded. Assuming that the populations are normally distributed with equal population variances, construct and interpret a 95% confidence interval estimate. Automated X1 = 53.4 hours S1 = 4.4 hours Manual X2 = 70.1 hours S2 = 4.2 hours The 95% confidence interval for the difference between the two population means for the length of time it takes to make a part from start to finish is (H1-H2) (Round to two decimal places as needed.)

Answer 1

solution:-

x1 = 53.5 , s1 = 4.4

x2 = 70.1 , s2 = 4.2

n1 = 16 , n2 = 16

degrees of freedom df = (n1+n2)-2 = (16+16)-2 = 30

the value of 95% confidence with df is t = 2.042

confidence interval formula

=>(x1-x2) +/- t * sqrt(s1^2/n1 + s2^2/n2)

=> (53.4 - 70.1) +/- 2.042 * sqrt((4.4^2/16) + (4.2^2/16))

=> -19.81 ≤ µ ≤ -13.59