Question

question 4
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 null hypothesis?
a. o the machine is not filling the boxes with the proper amount of cereal. the average is not 24 ounces.
b. o the machine fills the boxes with the proper amount of cereal. the average is 24 ounces.
c. o the machine is not putting enough cereal in the boxes. the average is less than 24 ounces.

Explanation:

Step1: Understand the null hypothesis concept

The null hypothesis \(H_0\) is a statement of no difference or no effect. In this context, it assumes the machine is working as intended.

Step2: Analyze each option

• Option A: “The machine is not filling the boxes with the proper amount of cereal. The average is not 24 ounces” is an alternative hypothesis (a statement of difference).
• Option B: “The machine fills the boxes with the proper amount of cereal. The average is 24 ounces” fits the null hypothesis as it assumes no issue (machine is working correctly with average 24 ounces).
• Option C: “The machine is not putting enough cereal in the boxes. The average is less than 24 ounces” is also an alternative hypothesis (a specific type of difference - less than).

So, the null hypothesis is Option B.

Answer:

B. The machine fills the boxes with the proper amount of cereal. The average is 24 ounces.