Which factor does NOT influence the power of a test?

In hypothesis testing, the power of a test is defined as the probability of correctly rejecting the null hypothesis when it is false. Several factors can influence the power of a test, including the sample size, the alpha level, and the standard deviation of the population. However, the mean of the sample does not directly influence the power.

The sample size is critical because larger samples provide more accurate estimates and increase the likelihood of detecting an effect if it exists. The alpha level, which is the threshold for rejecting the null hypothesis, also has a significant impact on power; decreasing the alpha level (making it more stringent) generally lowers the power, while increasing it raises the power. The standard deviation of the population affects the variability of the data; less variability (a smaller standard deviation) leads to increased power because it allows for clearer detection of an effect.

The mean of the sample, however, does not influence the power of the test in the same way. While the sample mean plays a role in determining the outcome of the hypothesis test, it does not inherently affect the ability of the test to detect an effect when one exists. The mean is a summary statistic that reflects the data collected, but it does not influence the parameters that affect power—such as sample