Question

1. 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 test results at least as extreme as the results actually observed, assuming the null hypothesis is correct. A low p - value (e.g., \(p<0.05\)) means that if the null hypothesis were true, the observed data (or more extreme data) would be very unlikely to occur.

• Option a: A low p - value has no relation to the test statistic being zero. The test statistic is calculated based on sample data and the hypothesized parameter, and its value alone does not determine the p - value in this simplistic way.
• 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 “definitely false”. A low p - value is evidence against the null hypothesis, not for its “definite truth”.

Answer:

d. The observed data are unlikely under the null hypothesis