Answer:
Explanation:
In a hypothesis test, there are two types of errors that can occur: Type I error and Type II error.
Type I Error (False Positive):
Definition: This error occurs when the null hypothesis is true, but we incorrectly reject it.
In the context of the voting example, a Type I error would mean concluding that the proportion of 18- to 29-year-old voters who voted in the 2018 election was higher when, in fact, it was not.
Probability of Type I Error: Denoted by the symbol α, it represents the significance level chosen for the test. Common values are 0.05 or 0.01. Lowering the significance level reduces the chance of Type I error but increases the chance of Type II error.
Type II Error (False Negative):
Definition: This error occurs when the null hypothesis is false, but we fail to reject it.
In the context of the voting example, a Type II error would mean failing to detect that the proportion of 18- to 29-year-old voters who voted in the 2018 election was higher when, in fact, it was.
Probability of Type II Error: Denoted by the symbol β, it depends on factors such as sample size, effect size, and the chosen significance level (α). Power of the test (1−β) is a related concept and represents the probability of correctly rejecting a false null hypothesis.