Question

A pet food producer 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 17 bags from line 1 and a random sample of 22 bags from line 2 were recently selected. Each bag's weight was measured and the accompanying table reports the summary measures from the samples. Assume the two lines are normally distributed with equal variances. Complete parts a through c below. Click the icon to view the table of summary statistics from the samples. a. Calculate the point estimate for the difference between the population means of the two lines. Point estimate=N b. Develop an 80% confidence interval estimate of the true mean difference between the two lines. The 80% confidence interval is (H1-H2) (Round to two decimal places as needed.) . c. Based on the 80% 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? Choose the correct answer below. O A. Since the interval does not contain zero, the two lines may fill bags with equal average amounts. The difference is at most about the magnitude of the lower limit. O B. Since the interval does not contain zero, the two lines do not fill bags with equal average amounts. The difference is at most about the magnitude of the upper limit O C. Since the interval does not contain zero, the two lines may fill bags with equal average amounts. The difference is at most about the magnitude of the upper limit. OD. Since the interval does not contain zero, the two lines do not fill bags with equal average amounts. The difference is at most about the magnitude of the lower limit. 0 Production Line Summary Statistics -X Click to select your answer(s). Sample Size, n Sample Mean, x Sample Standard Deviation, s Production Line 1 17 24.99 0.06 Production Line 2 22 25.25 0.09 Save for Later

Answer 1

The statistic software output for this problem is:

Two sample T summary confidence interval: Vi : Mean of Population 1 P2 : Mean of Population 2 H1 - H2 : Difference between two means (with pooled variances) 80% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit H1 - H2 -0.26 0.025332448 37 -0.29305516 -0.22694484

(a)

Point estimate = -0.26

(b)

A 80% CI is :

-0.29 -0.23

<μι – μ2 <

c)

B