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Power of a Test Remember: Type I error – Reject the H0 when you shouldn’t have. Type II error - Fail to reject the Ho you should have. when Fill in the chart with the type of error Null is True Null is False Reject Null Fail to Reject Null By choosing a level of significance ( ) we determine the probability of committing a type I error. 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 Ho. To increase the power of a test we Increase alpha Use a larger sample size. Null is True Null is False Reject Null Type I error (α) Correct decision (1-β) Fail to Reject Null Correct decision (1-α) Type II error (β) 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) 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?) 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?) Homework Worksheet