Hypothesis Tests for the Mean Differences between Populations When the Samples are not Independent (Paired Comparison Tests)

Authors

• Narayana Rao

Published

Creative Commons Attribution 3.0 License

Version 3

Last edited: 15 Dec 2010

Exported: 26 Nov 2011

Original URL: http://knol.google.com/k/-/-/2utb2lsm2k7a/492

Problem on Hand

 

100 recommendations of a stock broking firm are selected at random and are compared with return S&P 500 for the corresponding period. The average overperformance is 2.4%. The standard deviation of excess returns is 4.0%. The advisory firm claims that its recommendations outperform S&P by 3%. Verify at 5% level of significance.

 

We are trying to verify claims about the mean differences between the returns of the advisory firm’s stock selections and the corresponding returns on the S&P 500 index.

 

Step 1: Term the difference as d.

 

Null Hypo.   H0  =  Mu of  d = 3.0%

Alt. Hypo     H1  =  Mu of d is not equal to 3.0%

 

Standard error of d  =  S_d/S.R.(n)  =  4%/S.R.(100)

                                                    =  4/100 = .4%

T calculated  =  (d – Mu of d)/S_d = (2.4% - 3.0%) / 0.4%

                                           = -1.5

degrees of freedom  = n – 1 = 100-1 = 99

 

t critical = t (.025, 99)  = 1.984

 

Acceptance range for t is –1.984 to 1.984

T calculated is –1.5 and it is within acceptance range and hence null hypothesis is not rejected.

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Narayana Rao - 15 Dec 2010