The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices, such as scales, are accurate so customers and businesses are not cheated. Periodically, employees of the department go to businesses and test their scales. For example, a dairy bottles milk in 1-gallon containers. Suppose that if the filling process is working correctly, the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallon. The department's test process requires that they select a random sample of n = 9 containers. If the sample mean is less than 0.97 gallon, the department will fine the dairy. Based on this information, suppose that the dairy wants no more than a 0.05 chance of being fined, which of the following options exist if they can't alter the filling standard deviation?
A) They can convince the state to decrease the sample size.
B) They can change the mean fill level to approximately 1.025 gallons.
C) They could lower the mean fill level to a level lower than 1 gallon.
D) There is actually nothing that they can do if they can't modify the standard deviation.

Question

Quizplus · Accepted Answer

To reduce the chance of being fined to less than 0.05, the dairy can adjust the mean fill level to be higher than the current mean. By increasing the mean to approximately 1.025 gallons, they create a buffer that makes it less likely for the sample mean to fall below 0.97 gallons, even with the standard deviation remaining at 0.10 gallons. This approach does not require changing the standard deviation or the sample size; it simply adjusts the process mean to ensure compliance with the testing threshold.

The State Department of Weights and Measures Is Responsible for Making