Recall that the power (1 – β) of a hypothesis test is the probability that we will reject
the null hypothesis given that it is false; that is, the probability that we will correctly
reject the null hypothesis. All other things being equal, which of the following
changes to our hypothesis test will result in an increase of power? (Circle all that
apply.)
I. Increasing sample size
II. Decreasing sample size
III. Increasing the level of significance (α)
IV. Decreasing the level ofsignificance (α)
please explain
To determine which changes to a hypothesis test will result in an increase in power, let's go through each option and explain how it affects power:
I. Increasing sample size: Increasing the sample size generally leads to an increase in power. A larger sample size provides more information and reduces the variability in the data, making it easier to detect a true effect or difference from the null hypothesis.
II. Decreasing sample size: Decreasing the sample size would normally result in a decrease in power. With a smaller sample, there is less information available, leading to increased variability and a higher chance of missing a true effect.
III. Increasing the level of significance (α): Increasing the level of significance will not increase power. The level of significance (α) represents the threshold for rejecting the null hypothesis. It determines how much evidence is required to reject the null hypothesis. Increasing α simply allows more possible rejections, but it does not directly affect the ability to detect a true effect.
IV. Decreasing the level of significance (α): Decreasing the level of significance can increase power. By lowering α, the threshold for rejecting the null hypothesis becomes less strict. This means that smaller effect sizes or differences will be considered significant, leading to a higher chance of correctly rejecting the null hypothesis.
In summary, the changes that will result in an increase in power are:
- Increasing sample size (I)
- Decreasing the level of significance (α) (IV)
Therefore, you should circle options I and IV.