Question

the makers of mini - oats cereal have an automated packaging machine that is set to fill boxes with 24 ounces of cereal.at various times in the packaging process, we select a random sample of 100 boxes to see whether or not the machine is filling the boxes with an average of 24 ounces of cereal.which of the following is a statement of the alternative hypothesis?
a. the machine is not filling the boxes with the proper amount of cereal. the average is not 24 ounces.
b. the machine fills the boxes with the proper amount of cereal. the average is less than 24 ounces.
c. the machine fills the boxes with the proper amount of cereal. the average is 24 ounces.

Explanation:

In hypothesis testing, the alternative hypothesis ($H_1$) is what we are trying to find evidence for. The null hypothesis ($H_0$) is usually a statement of no - difference or equality. Here, the null hypothesis would be that the machine fills the boxes with an average of 24 ounces ($H_0:\mu = 24$). The alternative hypothesis is the opposite of the null hypothesis. Option A is a non - directional (two - tailed) alternative hypothesis, which is appropriate when we are just interested in whether the machine is not filling the boxes with the proper (24 - ounce) amount (it could be more or less). Option B is a one - tailed (left - tailed) hypothesis (only considering less than 24 ounces), and option C is a statement of the null hypothesis.

Answer:

A. The machine is not filling the boxes with the proper amount of cereal. The average is not 24 ounces.