How does increasing sample size affect the probability that a statistical test will reject the null hypothesis?

• A. It decreases the likelihood of rejecting the null hypothesis
• B. It increases the likelihood of rejecting the null hypothesis
• C. It has no effect on the likelihood
• D. It increases the likelihood only when the effect size is large

Answer: (B)

Increasing sample size increases the power of a statistical test, which is the probability of rejecting the null when there is a true effect. When you collect more data, the standard error (the amount of sampling variability) decreases. That makes the test statistic more likely to fall into the rejection region for any real effect, so the p-value tends to get smaller and you’re more likely to conclude there is a difference or effect. This improvement in power happens for effects of various sizes; it just depends on having enough data to detect them. If the null is true, keeping the significance level fixed keeps the Type I error rate at that level, but with a real effect, larger n makes it easier to detect it.