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

Statistical power is the probability that a test correctly picks up a real difference between two means. Two things push power up: more data, and a looser significance threshold.

1. Increase both samples from 100 to 1000: more observations narrow the spread of the sample mean, so real differences stand out more clearly against noise. This raises power.
2. Increase $\alpha$ from 0.01 to 0.2: a looser significance level means the test rejects the null hypothesis more easily, which raises the chance of catching a true effect, so power goes up (though false alarms go up too).
3. Decrease $\alpha$ from 0.2 to 0.01: a stricter significance level makes the test more cautious about rejecting the null, so it becomes harder to detect a true effect, and power falls.
4. Decrease both samples from 1000 to 100: fewer observations widen the spread of the sample mean, making true differences harder to see, so power falls.

Only the first two changes raise power, matching options (A) and (B).

Let's summarize:

• A bigger sample size increases power by shrinking the standard error.
• A larger significance level increases power by widening the rejection region.

So the conditions that raise power are (A) and (B).