What happens to statistical power when sample size increases?

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Multiple Choice

What happens to statistical power when sample size increases?

Explanation:
Power is the probability that a test will reject the null hypothesis when the alternative is true. As sample size grows, the standard error of the estimate shrinks (for example, the standard error of the mean is sigma divided by the square root of n). This makes the distribution of the test statistic under the true effect more separated from the null distribution, so the test is more likely to exceed the critical value if there is a real effect. In other words, the chance of detecting a true effect increases, reducing the probability of a Type II error. So, with larger samples, statistical power increases for a given effect size and significance level.

Power is the probability that a test will reject the null hypothesis when the alternative is true. As sample size grows, the standard error of the estimate shrinks (for example, the standard error of the mean is sigma divided by the square root of n). This makes the distribution of the test statistic under the true effect more separated from the null distribution, so the test is more likely to exceed the critical value if there is a real effect. In other words, the chance of detecting a true effect increases, reducing the probability of a Type II error. So, with larger samples, statistical power increases for a given effect size and significance level.

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