Question

question 8
which of the following facts about the p - value of a test is correct?
the p - value is calculated under the assumption that the null hypothesis is true.
the smaller the p - value, the more evidence the data provide against h0.
the p - value can have values between - 1 and 1.
all of the above are correct.
just (a) and (b) are correct.
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Explanation:

1. Analyze Option A: The p - value is calculated under the assumption that the null hypothesis ($H_0$) is true. This is a fundamental concept in hypothesis testing. When we calculate the p - value, we start with the assumption that $H_0$ holds, and then we find the probability of observing a test statistic as extreme or more extreme than the one we calculated from the sample data. So, Option A is correct.
2. Analyze Option B: The smaller the p - value, the more evidence we have against the null hypothesis $H_0$. For example, if the p - value is 0.01, it means that if $H_0$ were true, the probability of getting our observed result (or a more extreme one) is only 1%. This gives us strong evidence to reject $H_0$. If the p - value is 0.5, the probability of getting the result under $H_0$ is 50%, which is not very surprising, so we have little evidence against $H_0$. So, Option B is correct.
3. Analyze Option C: The p - value is a probability, and probabilities range from 0 to 1 (inclusive). A p - value cannot be less than 0 or greater than 1. So, the statement "The p - value can have values between - 1 and 1" is incorrect.
4. Analyze Option D: Since Option C is incorrect, "All of the above are correct" is also incorrect.
5. Analyze Option E: Since Option A and Option B are correct, "Just (A) and (B) are correct" is the right choice.

Answer:

E. Just (A) and (B) are correct