A paint manufacturer fills cans of paint using a machine that has been calibrated to fill the cans to contain an average $\mu$ of 1 gallon (128 ounces) each. To test whether their machine has come out of calibration, the manufacturer takes a random sample of 25 cans and finds that they average 128.2 ounces with a standard deviation of 2 ounces. Is this strong evidence that the filling machine is set too high and thus is no longer calibrated properly?
What are the null and alternative hypotheses in this situation?

Question

A paint manufacturer fills cans of paint using a machine that has been calibrated to fill the cans to contain an average

\mu

of 1 gallon (128 ounces) each. To test whether their machine has come out of calibration, the manufacturer takes a random sample of 25 cans and finds that they average 128.2 ounces with a standard deviation of 2 ounces. Is this strong evidence that the filling machine is set too high and thus is no longer calibrated properly?
What are the null and alternative hypotheses in this situation?

Quizplus · Accepted Answer

The null hypothesis (H0) is that the filling machine is calibrated properly and fills cans to contain an average of 128 ounces each. The alternative hypothesis (Ha) is that the machine is set too high and fills cans with more than 128 ounces on average. As we are checking whether the filling machine is set too high, the alternative hypothesis will be one-tailed and greater than the null hypothesis. Therefore, the correct choice is B.

A Paint Manufacturer Fills Cans of Paint Using a Machine μ\muμ

A Paint Manufacturer Fills Cans of Paint Using a Machine $\mu$