1. Power of a Test

2. Remember: Type I error – Reject the H 0 when you shouldn’t have. Type II error - Fail to reject the H o when you should have.

3. Fill in the chart with the type of error Null is TrueNull is False Reject Null Fail to Reject Null By choosing a level of significance ( ) we determine the probability of committing a type I error.

4. Power of a Test: (1 – β) It measures the sensitivity of the test to detect a real difference in parameters if one really exists. Rejecting a False H o.

5. To increase the power of a test we Increase alpha Use a larger sample size. Null is TrueNull is False Reject Null Type I error (α) Correct decision (1-β) Fail to Reject Null Correct decision (1-α) Type II error (β)

6. Cigarette manufacturer claims that the mean nicotine content of its cigarettes is 1.5 mg. Researchers believe it’s more than this. Test a sample of 36 and find standard deviation is 0.2. Use a 1% significance level. (Suppose it’s really 1.6)

7. A study claims that the mean weight of a book is 2.4 pounds. Researchers believe that it is more. Test a sample of 30 and st. dev. Is 0.5 pounds. Use 5% significance level. (What if it’s really 2.7 pounds?)

8. A study claims that the mean weight of a dog is 26.8 pounds. Researchers believe that it’s less than this. Test a sample of 36 and st. dev. Is 2.2 pounds. Use 5% significance level. (What if it’s really 26 pounds?)

9. Homework Worksheet