The p value is the:
a. probability with which a test statistic would occur if the research hypothesis were true.
b. probability with which a test statistic would occur if the null hypothesis were true.
c. cutoff probability at which a test statistic is considered extreme.
d. probability with which a test statistic would occur if both the null and research hypothesis
were false.
I think it is either b or c
The correct answer is b. The p-value is the probability with which a test statistic would occur if the null hypothesis were true. It represents the strength of evidence against the null hypothesis. When the p-value is very low (below a predetermined significance level), it suggests that the observed data is unlikely to have occurred by chance alone, and thus, provides support for rejecting the null hypothesis.
To determine which answer choice correctly describes the p-value, we should review some background information on hypothesis testing.
Hypothesis testing is a statistical technique used to make inferences about a population based on a sample. In this process, we have two competing hypotheses: the null hypothesis (H₀), which represents the absence of an effect or no difference between groups, and the alternative or research hypothesis (H₁), which suggests the presence of an effect or a difference between groups.
The p-value is a key concept in hypothesis testing. It represents the probability of obtaining a test statistic as extreme as the one observed in the sample, assuming the null hypothesis is true. In simpler terms, it measures the evidence against the null hypothesis.
Now, let's evaluate the answer choices:
a. probability with which a test statistic would occur if the research hypothesis were true.
This answer choice does not accurately describe the p-value. The p-value is specifically focused on the null hypothesis, not the research hypothesis.
b. probability with which a test statistic would occur if the null hypothesis were true.
This answer choice correctly describes the p-value. The p-value represents the probability of obtaining the observed test statistic if the null hypothesis were true. It is a measure of how likely we would see our results if the null hypothesis were actually correct.
c. cutoff probability at which a test statistic is considered extreme.
This answer choice does not accurately describe the p-value. The p-value is not a predetermined cutoff, but a calculated probability based on the data. It is used in hypothesis testing to make determinations about the significance of the results.
d. probability with which a test statistic would occur if both the null and research hypotheses were false.
This answer choice does not accurately describe the p-value. The p-value is focused on the null hypothesis and does not directly consider the research hypothesis.
Therefore, the correct answer to the question is b. The p-value represents the probability with which a test statistic would occur if the null hypothesis were true.