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?
Based on the P-value for a significance test in this situation, we should conclude
A) the null hypothesis provides a reasonable explanation of the data.
B) the alternative hypothesis provides a reasonable explanation of the data.
C) we should reject the null hypothesis at significance level 0.05.
D) the alternative hypothesis provides a reasonable explanation of the data, and we should reject the null hypothesis at significance level 0.05.

Question

Quizplus · Accepted Answer

The P-value in this context likely indicates that the difference between the sample mean (128.2 ounces) and the population mean (128 ounces) is not statistically significant, especially given the small sample size and the minor deviation. This suggests that the null hypothesis (that the machine is properly calibrated) cannot be rejected based on this evidence alone.

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

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