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.
What is your answer (guess)?
b or c
To determine the correct option, let's break down the definition of a p-value and how it relates to hypothesis testing.
In hypothesis testing, we make assumptions about a population based on sample data. Two competing hypotheses are formed: the null hypothesis (H0) and the alternative or research hypothesis (Ha). The null hypothesis assumes that there is no significant difference or relationship between variables, while the alternative hypothesis suggests otherwise.
The p-value is a measure of the evidence against the null hypothesis. It quantifies the probability of obtaining test results as extreme or more extreme than those observed, assuming that the null hypothesis is true. The p-value helps us make a decision about whether to reject or fail to reject the null hypothesis.
Now, let's consider each option:
a. Probability with which a test statistic would occur if the research hypothesis were true.
This option is incorrect. The p-value is based on the assumption that the null hypothesis is true, not the research hypothesis.
b. Probability with which a test statistic would occur if the null hypothesis were true.
This is the correct option. The p-value measures the probability of obtaining the observed data or more extreme data under the assumption that the null hypothesis is true.
c. Cutoff probability at which a test statistic is considered extreme.
This option refers to the critical value, which is typically determined before the hypothesis test. It is not the definition of a p-value.
d. Probability with which a test statistic would occur if both the null and research hypothesis were false.
This option is incorrect. The p-value does not consider both hypotheses being false; it reflects the probability of the test statistic occurring if the null hypothesis were true.
Therefore, the correct option is b. The p-value is the probability with which a test statistic would occur if the null hypothesis were true.