Which of the following will increase the power of a statistical test?

a. Change Ą from .05 to .01.
b. Change from a one-tailed test to a two-tailed test.
c. Change the sample size from n = 100 to n = 25.
d. None of the other options will increase power.

To determine which option will increase the power of a statistical test, let's review each option and explain how it affects the power of the test:

a. Change Ą from .05 to .01: The value of Ą, also known as the significance level, represents the maximum level of chance error that we are willing to accept. Decreasing the significance level from .05 to .01 means that we are becoming more strict in accepting statistical significance, and will require stronger evidence to reject the null hypothesis. While changing the significance level affects the likelihood of making a Type I error (rejecting the null hypothesis when it is actually true), it does not directly impact the power of the test. Therefore, changing Ą is not the correct option to increase power.

b. Change from a one-tailed test to a two-tailed test: In hypothesis testing, a one-tailed test focuses on specifically detecting an effect in one direction (either positive or negative), whereas a two-tailed test is used when we want to detect an effect regardless of its direction. By changing from a one-tailed test to a two-tailed test, we are expanding our scope and considering both positive and negative effects. This expansion may increase the power of the test because it allows for a larger range of possible outcomes to capture the effect. Therefore, changing from a one-tailed test to a two-tailed test can increase the power of the statistical test.

c. Change the sample size from n = 100 to n = 25: The sample size directly impacts the power of a statistical test. Increasing the sample size generally leads to a higher power as it provides more data points, which can reduce sampling error and increase the likelihood of detecting the effect. Conversely, reducing the sample size can decrease the power of the test, as there may be less reliable information to draw conclusions from. Therefore, changing the sample size from n = 100 to n = 25 will likely decrease the power, not increase it.

d. None of the other options will increase power: This option suggests that none of the previous options will increase power. However, as explained earlier, changing from a one-tailed test to a two-tailed test is a valid option that can increase power. Therefore, this option is not correct.

In conclusion, out of the given options, changing from a one-tailed test to a two-tailed test is the option that will increase the power of the statistical test.

To increase the power of a statistical test, we need to consider the options provided and determine which one(s) would increase the power.

a. Change Ą from .05 to .01: Changing Ą (the significance level) from .05 to .01 would decrease the likelihood of rejecting the null hypothesis, making it a more stringent test. This would actually decrease the power of the test, so option a is not correct.

b. Change from a one-tailed test to a two-tailed test: A two-tailed test is more powerful than a one-tailed test because it considers both tails of the distribution. By dividing the alpha (significance level) in half between each tail, the test is more likely to detect a significant difference. Therefore, changing from a one-tailed test to a two-tailed test would increase the power. So, option b is correct.

c. Change the sample size from n = 100 to n = 25: Increasing the sample size generally increases the power of a statistical test. With a larger sample size, there is more evidence to detect a significant difference. Therefore, changing the sample size from n = 100 to n = 25 would actually decrease the power, making option c incorrect.

d. None of the other options will increase power: This option is incorrect, as we have already identified that changing from a one-tailed test to a two-tailed test would increase the power.

In conclusion, the correct option that will increase the power of a statistical test is b. Change from a one-tailed test to a two-tailed test.

Choose d.

None of the other choices are correct.

Choice a: should read change alpha from .01 to .05.

Choice b: should read change from a two-tailed test to a one-tailed test.

Choice c: should read change sample size n = 25 to n = 100.