Question

A pet food producer manufactures and then fills 25-pound bags of dog food on two different production lines located in separate cities. In an effort to determine whether differences exist between the average fill rates for the two lines, a random sample of 22 bags from line 1 and a random sample of 25 bags from line 2 were recently selected. Each bag’s weight was measured and the following summary measures from the samples are reported:

Production Line 1

Sample size 22

Sample mean weight (lbs.) 24.89

Sample variance 0.0081

Production Line 2

Sample size25

Sample mean weight (lbs.) 25.03

Sample variance 0.0196

Construct a 96% confidence interval estimate of the average difference in fill weights for the 2 production lines. Interpret the practical meaning of the resulting confidence interval, in the context of the problem, in plain English.

Answer 1

DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

      = (0.0081/22 + 0.0196/25)^2/((0.0081/22)^2/21 + (0.0196/25)^2/24)

      = 41

At 96% confidence interval the critical value is t^* = 2.121

The 96% confidence interval for difference in means is

() +/- t^* * sqrt(s1^2/n1 + s2^2/n2)

= (24.89 - 25.03) +/- 2.121 * sqrt(0.0081/22 + 0.0196/25)

= -0.14 +/- 0.07

= -0.21, -0.07

We are 96% confident that the true average difference in fill weights for the two production lines lies between the confidence bound -0.21 and -0.07