3 calculatea 100 1 confidenceintervalestimatefor

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Unformatted text preview: of t ( n − 1 ) Lower Tail Area = 0.025 Upper Tail Area = 0.05 / 2 = 0.025 -tc 0 tc Reject H0 ← → d o n o t r e j e c t ← → Reject H0 4 Chapter 11 (2) Calculate a p‐value for the test as: p‐value = 2 ⋅ P(t ( n − 1 ) > t ) The decision rule is reject the null hypothesis if: p‐value < α The p‐value must be calculated with computer software. (3) Calculate a 100 (1 − α) % confidence interval estimate for the difference in population means μ X − μ Y . The method was presented in Chapter 9.1. The decision rule is to reject the null hypothesis of equal populations means if the value zero is not contained between the lower and upper limits of the confidence interval estimate. 5 Chapter 11 Example: The stock market data set introduced in Chapter 9.1 contained observations for 20 successive business days described by: x 1 , x 2 , . . . , x n daily percentage returns for a company, and y 1 , y 2 , . . . , y n daily percentage returns for a market portfolio. The differences are generated as: di = xi − yi for i = 1, 2, . . . , 20 The sample mean and standard deviation of the differences were calculated as: d =...
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