Question

1. which of the following best describes statistical significance in hypothesis testing?

a. the p - value is greater than 0.05
b. the result is unlikely to have occurred by chance, according to a pre - defined significance level
c. the test statistic equals zero
d. a large sample size

Explanation:

• Option a: If the p - value is greater than 0.05 (a common significance level), we fail to reject the null hypothesis, so it does not describe statistical significance.
• Option b: Statistical significance means that the result is unlikely to have occurred by chance. This is determined by comparing the p - value (probability of obtaining the result under the null hypothesis) with a pre - defined significance level (e.g., 0.05). If \(p\leq\alpha\) (significance level), the result is statistically significant.
• Option c: A test statistic of zero does not imply statistical significance. For example, in a t - test, a t - statistic of zero would mean that the sample mean is equal to the hypothesized population mean (in a one - sample t - test), but this is just a point estimate and does not account for the variability (the p - value is needed for significance).
• Option d: A large sample size can increase the power of a test (ability to detect a true effect), but it is not the definition of statistical significance. Statistical significance is about the probability of the result under the null hypothesis, not the sample size per se.

Answer:

B. The result is unlikely to have occurred by chance, according to a pre - defined significance level