Question

An automated machine is calibrated to fill bags of pretzels so that each bag weighs 8 ounces. A worker at the factory believes the machine is not filling the bags to the correct weight. She randomly selects 40 bags of pretzels and, after weighing them, calculates their mean weight to be 8.4 ounces. Write null and alternative hypothesis to describe this situation.

Answer 1

The null hypothesis (H0) is that the machine is filling the bags of pretzels to the correct weight, that is, the mean weight of the bags is 8 ounces:

H0: μ = 8

The alternative hypothesis (Ha) is that the machine is not filling the bags to the correct weight, that is, the mean weight of the bags is different from 8 ounces:

Ha: μ ≠ 8

In this case, the worker's observation of a mean weight of 8.4 ounces in a sample of 40 bags suggests that the bags may be overfilled. To test this hypothesis, the worker would need to conduct a hypothesis test using appropriate statistical methods and a significance level to determine whether the observed difference is statistically significant or not.