Question

A researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18 ounce boxes is less than 18 ounces. He uses the following hypotheses: H 0: μ = 18 vs H A: μ < 18 and finds a P-value of 0.01. Draw a conclusion about the cereal box weight at a significance level of 0.05.

Answer 1

We conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Explanation:

We are given that a researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Let
`\mu` = mean weight of cereal in its 18-ounce boxes.

So, Null Hypothesis,
`H_0` :
`\mu` = 18 {mean that the mean weight of cereal in its 18-ounce boxes is equal to 18 ounces}

Alternate Hypothesis,
`H_A` :
`\mu` < 18 {mean that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces}

Also, it is given that the P-value is 0.01 and the level of significance is 0.05.

The decision rule based on the P-value is given by;

• If the P-value of our test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.

• If the P-value of our test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis as our test statistics will not fall in the rejection region.

Here, clearly our P-value is less than the level of significance as 0.01 < 0.05, so we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.

Therefore, we conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.