Final answer:
Statistical power is related to Type II errors, not Type I errors. It represents the likelihood of correctly rejecting a false null hypothesis, with higher power indicating a lower probability of a Type II error. Type I error levels are set by the significance level, not affected by the power of the test.
Step-by-step explanation:
The statement that statistical power tells us our level of Type I error is false. Statistical power, in fact, is concerned with the probability of correctly rejecting a false null hypothesis, which is related to the Type II error. The power of a statistical test is calculated as 1 minus the probability of a Type II error (β), so if the power is high, the chance of a Type II error is low. On the other hand, a Type I error (α) occurs when the null hypothesis is incorrectly rejected when it is actually true. The level of Type I error is controlled by the significance level of the test, often set at 5% or 0.05. Increasing the sample size is one method of increasing the power of a test, which thereby reduces the risk of a Type II error, not a Type I error.