Quantitative techniques for Economic Analysis II Preetha Rachel George Department of Statistics Module IV Testing of hypothesis Statistical test of a hypothesis is a rule or procedure which makes one to decide about the acceptance or rejection of the hypothesis ID: 1034303
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1. M.A Economics Semester IIQuantitative techniques for Economic Analysis IIPreetha Rachel GeorgeDepartment of Statistics
2. Module IVTesting of hypothesisStatistical test of a hypothesis is a rule or procedure which makes one to decide about the acceptance or rejection of the hypothesis.
3. Null hypothesis - The hypothesis that is to be tested , usually denoted by the symbol H0A null hypothesis is a definite statement about the population parameter which is usually a hypothesis of no difference.Eg:- To test whether the population mean μ has a specified mean μ0 , then H0 : μ = μ0
4. Alternative hypothesis :- Complementary to the null hypothesis, denoted by H1 Eg:- If H0 : μ = μ0 , then H1 could be H1 : μ ≠ μ0 or μ > μ0 or μ < μ0
5. Simple hypothesis – specifies the population completely. Eg :- For N (μ, σ ), H0 : μ = μ0 , σ = σ 0 Composite hypothesis – does not specify the population completely.Eg :- H0 : μ = μ0 or H0 : μ = μ0 , σ < σ 0
6. Type I error – rejecting H0 when H0 is true.P(rejecting H0 / H0 ) = P ( type I error ) = αType II error – accepting H0 when H0 is false. P(accepting H0 / H1 ) = P( type II error ) = βα and β are also known as producer’s risk and consumer’s risk respectively.
7. Critical region or rejection region – area under the sampling distribution in which the test statistical value has to fall for the null hypothesis to be rejected.The remaining region is known as acceptance region.
8. Level of significance or size of the test - P ( type I error ) , α .Power of a test - P(rejecting H0 / H1 ) = 1- P(accepting H0 / H1 ) = 1 - P( type II error ) = 1- β
9. One tailed test – One sided alternative to H0Eg:- testing H0 : μ = μ0 against H1 : μ > μ0 or H1 : μ < μ0Two tailed test – Two sided alternative to the null hypothesis.Eg:- testing H0 : μ = μ0 against H1 : μ ≠ μ0
10. Procedure for testing of hypothesisSet up H0 and H1Decide whether one tailed or two tailed testChoose an appropriate α.Choose the test statistic ‘t’ and specify its sampling distribution.Compare the value of ‘t’ with the critical value at the given level of α and accept or reject H0.