Answer:
We conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.
Step-by-step 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
= <em><u>mean weight of cereal in its 18-ounce boxes</u></em>.
So, Null Hypothesis,
:
= 18 {mean that the mean weight of cereal in its 18-ounce boxes is equal to 18 ounces}
Alternate Hypothesis,
:
< 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.
<u>The decision rule based on the P-value is given by;</u>
- If the P-value of our test statistics is less than the level of significance, then we have <em>sufficient evidence to reject our null hypothesis </em>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 <em>insufficient evidence to reject our null hypothesis</em> 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 <em>sufficient evidence to reject our null hypothesis </em>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.