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A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a P-value of 0.14.

In this context, what does the "14%" represent?

Choose the correct answer below:

A. If in fact the mean cholesterol of pizza eaters indicates a health risk, then only 14 of every 100 samples would have mean cholesterol levels as high (or higher) as observed in this sample.

B. If in fact the mean cholesterol of pizza eaters indicates a health risk, then only 14 of every 100 people who eat frozen pizza will have a cholesterol level that exceeds the value considered to indicate a health risk.

C. If in fact the mean cholesterol of pizza eaters does not indicate a health risk, then only 14 of every 100 samples would have mean cholesterol levels as high (or higher) as observed in this sample.

D. If in fact the mean cholesterol of pizza eaters does not indicate a health risk, then only 14 of every 100 people who eat frozen pizza will have a cholesterol level that exceeds the value considered to indicate a health risk.



Answer :

GinnyAnswer
To understand what the P-value of 0.14 represents in this context, let's break down the meaning of the P-value in hypothesis testing:

1. Definition of P-value: The P-value is the probability of obtaining results as extreme as, or more extreme than, the ones observed, assuming that the null hypothesis is true.

2. Null Hypothesis (H₀): In this scenario, the null hypothesis is that the mean cholesterol level among those who eat frozen pizza does not indicate a health risk.

3. Meaning of 0.14 P-value: A P-value of 0.14 means that there is a 14% probability of observing a sample mean cholesterol level as high as (or higher than) the one obtained in the study, if the null hypothesis is true.

Now, let's evaluate each choice:

- Choice A: Talks about the scenario where the mean cholesterol of pizza eaters indicates a health risk. However, in hypothesis testing, the P-value calculation assumes the null hypothesis is true, which is that the mean cholesterol level does not indicate a health risk. Therefore, this choice is incorrect.

- Choice B: Also makes the assumption that the mean cholesterol indicates a health risk and discusses individual cholesterol levels, which is not an interpretation of the P-value. This choice is incorrect.

- Choice C: Correctly states that if the mean cholesterol of pizza eaters does not indicate a health risk, then 14 of every 100 samples would have mean cholesterol levels as high (or higher) as the one observed. This aligns with the proper interpretation of the P-value.

- Choice D: Similar to the previous incorrect choices, this option is about individual cholesterol levels rather than sample mean cholesterol levels and assumes the null hypothesis states that cholesterol levels indicate health risk. This is incorrect.

So, based on this analysis, the correct interpretation of the P-value (0.14) in the given context is:
Choice C: "If in fact the mean cholesterol of pizza eaters does not indicate a health risk, then only 14 of every 100 samples would have mean cholesterol levels as high (or higher) as observed in this sample."

Therefore, the correct answer is:
OC (Choice C).

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