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 19 bags from line 1 and a random sample of 23 bags from line 2 were recently selected. Each bag’s weight was measured and the following summary measures from the samples are reported:

Production Production Line 1 Line 2 Sample Size, n 19 23 Sample Mean,–x24.96 25.01 Sample Standard Deviation, s 0.07 0.08 Management believes that the fill rates of the two lines are normally distributed with equal variances.

a. Calculate the point estimate for the difference between the population means of the two lines.

b. Develop a 95% confidence interval estimate of the true mean difference between the two lines.

c. Based on the 95% confidence interval estimate calculated in part

b, what can the managers of the production lines conclude about the differences between the average fill rates for the two lines?