Presentation on theme: " When we perform a hypothesis test, we make a decision to either Reject the Null Hypothesis or Fail to Reject the Null Hypothesis. There is always the."— Presentation transcript:
When we perform a hypothesis test, we make a decision to either Reject the Null Hypothesis or Fail to Reject the Null Hypothesis. There is always the possibility that we made an incorrect decision. We can make an incorrect decision in two ways:
1. If we reject the null when in fact the null is true, this is a Type I error 2. If we fail to reject the null when in fact the null is false, this is a Type II error.
A Type I error is the mistake of rejecting the null hypothesis when it is true. In testing for a medical disease, the null hypothesis is usually the assumption that a person is healthy. A Type I error is a false positive; a healthy person is diagnosed with the disease. The probability of rejecting the null hypothesis when it is true is equal to the alpha-level of the test. If alpha =.05, in the long-run, we will incorrectly reject the null hypothesis when it is really true about 5% of the time.
A type II error is made when we fail to reject the null hypothesis when it is false and the alternative is true. Prob(Type II Error) = In medical testing for a disease, this would be equivalent to a person who has the disease being diagnosed as disease free. This is called a false negative. Our ability to detect a false hypothesis is called the power of the test. The Power of a Test is the probability that it correctly rejects a false null hypothesis. Power = 1 - Prob (Type II Error) or
Ex: Let, and. Describe both types of error and their consequences.
A new car had been released for which the manufacturer reports that the car gets 23mpg for city driving. A consumer group feels that the true mileage is lower and performs the following hypothesis test, using α =.05. Assumptions: The gas mileage in the sample of 30 cars comes from an SRS drawn from the population of all mileage and the standard deviation is known, δ = 1.2. Null and alternate hypothesis: What is a Type I error in the context of this problem? What is a Type II error in the context of this problem?
The Probability of Type I error is, ! The Probability of Type II error is, and is dependent upon the following