Reason for rejecting Ho 拒绝无效假设的原因 Sampling Distribution 小概率事件原理 It is unlikely that we would Therefore we get a sample reject the null mean of this hypothesis that value u=50 ifin fact this were the population mean. 20 凡=50 Sample Mean H 0
m = 50 Sample Mean Sampling Distribution It is unlikely that we would get a sample mean of this value ... ... if in fact this were the population mean. ... Therefore, we reject the null hypothesis that m = 50. 20 H0 Reason for Rejecting H0 拒绝无效假设的原因 小概率事件原理
Level of significance. a 显著性水平 Defines Unlikely Values of Sample Statistic if Null Hypothesis Is True n Called rejection Region of Sampling Distribution Designated a(alpha) o Typical values are 0.01, 0.05,0.10 Selected by the researcher at the Start Provides the Critical Value(s)of the Test
• Defines Unlikely Values of Sample Statistic if Null Hypothesis Is True Called Rejection Region of Sampling Distribution • Designated a (alpha) Typical values are 0.01, 0.05, 0.10 • Selected by the Researcher at the Start • Provides the Critical Value(s) of the Test Level of Significance, a 显著性水平
Level of significance, a and the rejection Region u=3 +Critical H1:μ<3 Value(s) Rejection 0 Regions H(n:|=3 拒绝域 H1:μ>3 2 H H1:μ3
Level of Significance, a and the Rejection Region H0 : m =3 H1 : m < 3 0 0 0 H0 : m=3 H1 : m > 3 H0 : m = 3 H1 : m 3 a a a/2 Critical Value(s) Rejection Regions 拒绝域
Errors in Making decisions 决策错误 ype I Error(型错误) o Reject True Null Hypothesis o Has Serious Consequences o Probability of Type I Error Is a o Called Level of significance Type II Error(I型错误) a Do Not Reject False Null Hypothesis a Probability of Type lI Error Is B (Beta)
• Type I Error(I型错误） Reject True Null Hypothesis Has Serious Consequences Probability of Type I Error Is a ⚫ Called Level of Significance • Type II Error（II型错误） Do Not Reject False Null Hypothesis Probability of Type II Error Is b (Beta) Errors in Making Decisions 决策错误
Result possibilities Ho. Innocent Jury Trial Hypothesis Test Actual Situation Actual situation Verdict Innocent Guilty Decision Ho True Ho False Do Not Innocent Correct| Error Reject Type ll 1-a Error(B) Guilty Error Correc/ Reject ype I Power Error (1-β)
H0 : Innocent Jury Trial Hypothesis Test Actual Situation Actual Situation Verdict Innocent Guilty Decision H0 True H0 False Innocent Correct Error Do Not Reject H0 1 - a Type II Error (b ) Guilty Error Correct Reject H0 Type I Error (a ) Power (1 - b) Result Possibilities