Question

1. what does a low p - value (typically less than 0.05) indicate in hypothesis testing?

a. the null hypothesis is definitely true
b. the observed data are unlikely under the null hypothesis
c. there is a 5% chance the data are correct
d. the test statistic is zero

Explanation:

In hypothesis testing, the p - value is the probability of obtaining the observed data (or more extreme data) if the null hypothesis is true. A low p - value (e.g., less than 0.05) means that the observed data is unlikely to occur under the assumption that the null hypothesis is true.

• Option a: A low p - value does not mean the null hypothesis is definitely true. In fact, it provides evidence against the null hypothesis.
• Option c: 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 d: A low p - value has no direct relation to the test statistic being zero. The test statistic is used to calculate the p - value, but a non - zero test statistic can result in a low p - value.

Answer:

B. The observed data are unlikely under the null hypothesis