Question

Which of the following conditions result(s) in a higher statistical power for comparing means of two samples using t-test?

• A. An increase in the sizes of both the samples from 100 to 1000
• B. An increase in the significance level from \(\alpha = 0.01\) to \(\alpha = 0.2\)
• C. A decrease in the significance level from \(\alpha = 0.2\) to \(\alpha = 0.01\)
• D. A decrease in the sizes of both the samples from 1000 to 100

Hint:

Power rises with a bigger sample and a looser significance level, and falls with the opposite changes.

Answer 1

The Correct Option is A, B

Step 1: Recall what statistical power means.
Statistical power is the chance of correctly rejecting a false null hypothesis.
In a t-test comparing two means, power grows when the test can pick out a true difference more easily.

Step 2: Recall what changes power.
Power rises with a larger sample size, because a bigger sample shrinks the standard error of the mean and makes small true differences stand out.
Power also rises with a larger significance level \(\alpha\), because a bigger \(\alpha\) widens the rejection region, making it easier to reject the null hypothesis (at the cost of more false positives).

Step 3: Check each option.
Option (A): raising both sample sizes from 100 to 1000 shrinks the standard error, so power goes up. This is correct.
Option (B): raising \(\alpha\) from 0.01 to 0.2 widens the rejection region, so power goes up. This is correct.
Option (C): lowering \(\alpha\) from 0.2 to 0.01 narrows the rejection region, so power goes down, not up. This is wrong.
Option (D): shrinking both sample sizes from 1000 to 100 raises the standard error, so power goes down, not up. This is wrong.

Final Answer:
A bigger sample size and a larger significance level both raise the power of the t-test. \[ \boxed{\text{(A), (B)}} \]