Outcomes and Probabilities Possible Hypothesis Test Outcomes Actual Situation Decision Ho True Ho False Do Not Reject No error Type ll Error Key: 1-a) (B) Outcome Ho (Probability) Reject Type I Error No Error Ho (a) Power=(1-B) Confidence Coefficient:is the probability that the null hypothesis is not rejected when in fact it is true and should not be rejected.The confidence level of a hypothesis test is(1-Confidence Value denoted by 1-a)100% Statistics fo agers Using Microsoft Excel Chap 8-16
Statistics for Managers Using Microsoft Excel Chap 8-16 Outcomes and Probabilities Actual Situation Decision Do Not Reject H0 No error (1 - ) Type II Error ( β ) Reject H0 Type I Error ( ) Possible Hypothesis Test Outcomes H0 True H0 False Key: Outcome (Probability) No Error Power=( 1 - β ) Confidence Coefficient: is the probability that the null hypothesis is not rejected when in fact it is true and should not be rejected. The confidence level of a hypothesis test is (1-Confidence Value denoted by 1- )100%
Type I ll Error Relationship Type I and Type ll errors can not happen at the same time Type I error can only occur if Ho is true Type ll error can only occur if Ho is false If Type I error probability (a),then Type ll error probability(B) Statistics for Managers Using Microsoft Excel Chap 8-17
Statistics for Managers Using Microsoft Excel Chap 8-17 Type I & II Error Relationship Type I and Type II errors can not happen at the same time Type I error can only occur if H0 is true Type II error can only occur if H0 is false If Type I error probability ( ) , then Type II error probability ( β )
Factors Affecting Type ll Error All else equal, B when the difference between hypothesized parameter and its true value ·BT when a ·BT when oT ·BT when n Statistics for nagers Using Microsoft Excel Chap 8-18
Statistics for Managers Using Microsoft Excel Chap 8-18 Factors Affecting Type II Error All else equal, β when the difference between hypothesized parameter and its true value β when β when σ β when n
Hypothesis Tests for the Mean Hypothesis Tests for u o Known o Unknown Statistics for Managers Using Microsoft Excel Chap 8-19
Statistics for Managers Using Microsoft Excel Chap 8-19 Hypothesis Tests for the Mean Known Unknown Hypothesis Tests for
Z Test of Hypothesis for the Mean (o Known) Convert sample statistic (X )to a Z test statistic Hypothesis Tests for u o Known o Unknown The test statistic is: Z X-μ 0 n Statistics for Ma agers Using Microsoft Excel Chap 8-20
Statistics for Managers Using Microsoft Excel Chap 8-20 Z Test of Hypothesis for the Mean (σ Known) Convert sample statistic ( ) to a Z X test statistic The test statistic is: n σ X μ Z σ Known σ Unknown Hypothesis Tests for