1. A sampling distribution describes the variability among average weights from day to day.
2. Before using a normal model for the sampling distribution of the average package weights, the manager must confirm that weights of individual packages are normally distributed.
3. A Type I error occurs if the mean weight m and standard deviation s do not change.
4. If the average weight of packages increases and the manager does not recognize the change, then the manager has committed a Type II error.
5. The standard error of the daily average is SE(X-bar) = 1.
6. An X-bar chart with control limits at 12 pounds and 32 pounds has a 5% chance of a Type I error.
7. To have a small chance for a Type II error, the manager of the warehouse should locate the control limits in the X-bar chart at 22 ± 3 pounds.
8. By expanding the control limits in the X-bar chart from 22 ± 2 to 22 ± 4 pounds, the manager reduces the chance of a Type I error by 50%.
The manager of a warehouse monitors the volume of shipments made by the delivery team. The automated tracking system tracks every package as it moves through the facility. A sample of 25 packages is selected and weighed every day. On the basis of contracts with customers, the mean weight should be μ = 22 pounds with σ = 5 pounds.