Question

what does a low p - value (typically less than 0.05) indicate in hypothesis testing?
a. the test statistic is zero
b. there is a 5% chance the data are correct
c. the null hypothesis is definitely true
d. the observed data are unlikely under the null hypothesis

Explanation:

In hypothesis testing, the p - value is the probability of obtaining results as extreme as, or more extreme than, the observed data, assuming the null hypothesis is true. A low p - value (e.g., < 0.05) means that if the null hypothesis were true, the observed data (or more extreme data) would be very unlikely.

• Option a: A low p - value does not imply the test statistic is zero. The test statistic is calculated based on sample data and is used to compute the p - value.
• Option b: The p - value is not about the chance that the data are correct. It is about the compatibility of the data with the null hypothesis.
• Option c: Hypothesis testing does not prove the null hypothesis is definitely true or false. We either reject or fail to reject the null hypothesis based on evidence.
• Option d: This is the correct interpretation. A low p - value indicates that the observed data are unlikely under the null hypothesis, which gives us evidence to reject the null hypothesis.

Answer:

d. The observed data are unlikely under the null hypothesis