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
To determine the correct answer, let's break down what the p-value represents in hypothesis testing.
When conducting a hypothesis test, we have a null hypothesis (H0) and an alternative or research hypothesis (Ha). The null hypothesis suggests that there is no significant effect or relationship, while the research hypothesis suggests the presence of a significant effect or relationship.
The p-value is a statistical measure that helps us determine the strength of evidence against the null hypothesis. It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed one, assuming the null hypothesis is true.
Now let's evaluate the options:
a. "probability with which a test statistic would occur if the research hypothesis were true" - This statement is incorrect. The p-value does not directly relate to the probability of the research hypothesis being true.
b. "probability with which a test statistic would occur if the null hypothesis were true" - This option is correct. The p-value calculates the probability of observing a test statistic as extreme as, or more extreme than, the observed one, assuming the null hypothesis is true. A lower p-value indicates stronger evidence against the null hypothesis.
c. "cutoff probability at which a test statistic is considered extreme" - This option is incorrect. The p-value itself is not a predefined cutoff; instead, it is compared to a predetermined significance level (usually denoted as alpha) to make a decision about the null hypothesis. If the p-value is less than or equal to the significance level, the null hypothesis is rejected.
d. "probability with which a test statistic would occur if both the null and research hypothesis were false" - This statement is incorrect. The p-value does not relate to the probability of both the null and research hypotheses being false.
Therefore, based on the explanations above, option b is the correct answer: the p-value represents the probability with which a test statistic would occur if the null hypothesis were true.