P-value Approach for Test Conclusion Under the assumption that H0 is true, the probability that the test statistic would take a value as extreme or more extreme than that actually observed is called the P-value of the test. Small P-value gives evidence against H0. Large P-value gives no evidence against H0. In general, the smaller the P-value the stronger the evidence against H0 provided by the data. The decisive value of the P is the significance level . week 8

Example week 8

Decision Errors When we perform a hypothesis test we hope that our decision will be correct, but sometimes it will be wrong. There are two possible errors that can be made in hypothesis test. The error made by rejecting the null hypothesis H0 when in fact H0 is true is called a type I error. The probability of making a type I error is denoted by . The error made by failing to reject the null hypothesis H0 when in fact H0 is false is called a type II error. The probability of making a type II error is denoted by . week 8

Significance level and type I error The significance level  of any test is the P(Type I error). week 8

Power The probability of rejecting H0 when a particular alternative value of the parameter is true is called the power of the test to detect that alternative. The power of a test against a particular alternative is Power = 1- β = 1- P( not rejecting H0 when H0 is false) = = P( rejecting H0 when H0 is false) week 8

Example week 8