Chapter 9 3 Testing Errors ♦Rejecting H0when it is true is defined as a Type I Error.α= significance level= size of test = P(Type I Error) = P(reject H0when H0is true) Note: confidence level= 1- α♦Failing to reject the H0when it is false is defined as a Type II error. β= P(Type II Error) = P(fail to reject H0when H0is false) Note: The powerof a statistical test is the probability of rejecting the null hypothesis H0when the alternative hypothesis is true. Power = 1 - βDecision H0is True H0is FalseFail to reject H0No error Type II ErrorReject H0Type I Error No errorChapter 9 4 Example (revisited)
Test the manufacturer's claim. H0: H1: Decision Criteria: 1) Suppose that if 60 ≤x≤68, we will fail to reject H0. 2) If x< 60 or x> 68, we will reject H0in favor of H1.Notes: (a)Values less than 60 and greater than 68 define the critical region(or regionof rejection) for the test. (b)The interval 60 ≤x≤68 is called the region of nonrejection. (c)60 and 68 are called the critical values. (d)A decision will be made based on the mean of a single sample taken from the steel.