Parameter Estimation and Evaluation Introduction to Hypothesis Testing Introduction to Hypothesis Testing Definition 2(9.2)[Simple Hypothesis Versus Composite Hypothesis] A hypothesis is simple if and only if it contains exactly one population.If the hypothesis contains more than one popula- tion,it is called a composite hypothesis. Remarks In Example 9.1,Ho contains only one parameter value, so Ho is a simple hypothesis.In contrast,the null hy- potheses in Examples 9.2 and 9.3 contain more than one parameter values,so they are composite hypotheses. Hypothesis Testing Introduction to Statistics and Econometrics July7,2020 11/110
Parameter Estimation and Evaluation Hypothesis Testing Introduction to Statistics and Econometrics July 7, 2020 11/110 Introduction to Hypothesis Testing Introduction to Hypothesis Testing Definition 2 (9.2) [Simple Hypothesis Versus Composite Hypothesis] Remarks
Parameter Estimation and Evaluation Introduction to Hypothesis Testing Introduction to Hypothesis Testing Definition 3(9.3)[Hypothesis Testing] A hypothesis testing procedure or a hypothesis test is a deci- sion rule that specifies .(1)for what sample values xm the decision is made to accept Ho as true,and .(2)for what sample values x"Ho is rejected and HA is accepted as true. Hypothesis Testing Introduction to Statistics and Econometrics July7,2020 12/110
Parameter Estimation and Evaluation Hypothesis Testing Introduction to Statistics and Econometrics July 7, 2020 12/110 Introduction to Hypothesis Testing Introduction to Hypothesis Testing Definition 3 (9.3) [Hypothesis Testing]
Parameter Estimation and Evaluation Introduction to Hypothesis Testing Introduction to Hypothesis Testing Remarks: The key to the construction of the decision rule for a hypothesis testing procedure is to determine the rules of rejection or acceptance of the null hypothesis. Hypothesis Testing Introduction to Statistics and Econometrics Juy7,2020 13/110
Parameter Estimation and Evaluation Hypothesis Testing Introduction to Statistics and Econometrics July 7, 2020 13/110 Introduction to Hypothesis Testing Introduction to Hypothesis Testing Remarks:
Parameter Estimation and Evaluation Introduction to Hypothesis Testing Introduction to Hypothesis Testing Definition 4(9.4)[Critical Region or Rejection Region] The set C of the sample points of the random sample X"for which Ho will be rejected is called the rejection region or critical region.The complement of the rejection region is called the acceptance region. Hypothesis Testing Introduction to Statistics and Econometrics July7,2020 14/110
Parameter Estimation and Evaluation Hypothesis Testing Introduction to Statistics and Econometrics July 7, 2020 14/110 Introduction to Hypothesis Testing Introduction to Hypothesis Testing Definition 4 (9.4) [Critical Region or Rejection Region]
Parameter Estimation and Evaluation Introduction to Hypothesis Testing Introduction to Hypothesis Testing Remarks: A standard approach to hypothesis testing is to choose a statistic T(Xm) and use it to divide the sample space of Xm into two mutually exclusive and exhaustive regions An(c)={x":T(x")≤c} and Cn(c)={x":T(x")>c} for some prespecified constant c. The first region,An(c),is the acceptance region,and the second,Cn(c),is the rejection region.The cutoff point c is called the critical value and T(Xm) is called a test statistic. An important issue in hypothesis testing is to determine a suitable value of c given a data set x".In general,we need to know the sampling distribution of T(X")under Ho in order to determine the threshold value c. Hypothesis Testing Introduction to Statistics and Econometrics July7,2020 15/110
Parameter Estimation and Evaluation Hypothesis Testing Introduction to Statistics and Econometrics July 7, 2020 15/110 Introduction to Hypothesis Testing Introduction to Hypothesis Testing Remarks: