Final answer:
The probability of correctly rejecting a false null hypothesis with an alpha of 0.05 and beta of 0.75 is 25%, which is the power of the test.
Step-by-step explanation:
The student's question is referring to statistical hypothesis testing concepts, specifically the probability of making a correct decision when testing a hypothesis. The values alpha (α = 0.05) and beta (β = 0.75) are given. Alpha is the probability of a Type I error, which is the error made by rejecting a true null hypothesis. Beta is the probability of a Type II error, which is the error made by failing to reject a false null hypothesis.
The probability of correctly rejecting a false null hypothesis is known as the power of the test, which is calculated as 1 minus beta (1 - β). In this case, the power is 1 - 0.75 = 0.25, or 25%. This means that there is a 25% chance of correctly rejecting a false null hypothesis using this test with the given alpha and beta levels.