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FEC 512.05
1. Introduction to Hypothesis Testing Istanbul Bilgi University FEC 512 Financial Econometrics-I Asst. Prof. Dr. Orhan Erdem
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9. Population Claim: the population mean age is 50. (Null Hypothesis: REJECT Suppose the sample mean age is 20: x = 20 Sample Null Hypothesis 20 likely if = 50? Is Hypothesis Testing Process If not likely, Now select a random sample H 0 : = 50 ) x
10. Reason for Rejecting H 0 Sampling Distribution of x = 50 If H 0 is true If it is unlikely that we would get a sample mean of this value ... ... then we reject the null hypothesis that = 50. 20 ... if in fact this were the population mean… x
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12. Level of Significance and the Rejection Region H 0 : μ ≥ 50 H 1 : μ < 50 0 H 0 : μ ≤ 50 H 1 : μ > 50 Represents critical value Lower-tail test Level of significance = 0 Upper-tail test Two-tail test Rejection region is shaded /2 0 /2 H 0 : μ = 50 H 1 : μ ≠ 50
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15. Outcomes and Probabilities Actual Situation Decision Do Not Reject H 0 No error (1 - ) Type II Error ( β ) Reject H 0 Type I Error ( ) Possible Hypothesis Test Outcomes H 0 False H 0 True Key: Outcome (Probability) No Error ( 1 - β )
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19. Level of Significance and the Rejection Region H 0 : μ ≥ 50 H A : μ < 50 50 H 0 : μ ≤ 50 H A : μ > 50 H 0 : μ = 50 H A : μ ≠ 50 /2 Lower tail test Level of significance = 50 /2 Upper tail test Two tailed test 5 0 - ? ? - ? ? Reject H 0 Reject H 0 Reject H 0 Reject H 0 Do not reject H 0 Do not reject H 0 Do not reject H 0 Example: Example: Example:
20. Level of Significance and the Rejection Region H 0 : μ ≥ 50 H A : μ < 50 0 H 0 : μ ≤ 50 H A : μ > 50 H 0 : μ = 50 H A : μ ≠ 50 /2 Lower tail test Level of significance = 0 /2 Upper tail test Two tailed test 0 -z α z α -z α /2 z α /2 Reject H 0 Reject H 0 Reject H 0 Reject H 0 Do not reject H 0 Do not reject H 0 Do not reject H 0 Example: Example: Example:
21. Upper Tail Tests Reject H 0 Do not reject H 0 z α 0 μ 0 H 0 : μ ≤ μ 0 H 1 : μ > μ 0 Critical value Z Alternate rule:
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28. Calculating the Test Statistic Known Large Samples Unknown Hypothesis Tests for Small Samples The test statistic is: But is sometimes approximated using a z: (continued)
29. Calculating the Test Statistic Known Large Samples Unknown Hypothesis Tests for Small Samples The test statistic is: (The population must be approximately normal) (continued)
![What is a Hypothesis? ,[object Object],[object Object],[object Object],[object Object],Example: The mean age of the citizens of this city is = 50.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)