The attached data on annual rates of return were collected from eleven randomly

Question

The attached data on annual rates of return were collected from eleven randomly selected stocks listed on the New York Stock Exchange (“the big board”) and twelve randomly selected stocks listed on NASDAQ. Assume the population standard deviations are the same. At the 0.01 significance level, can we conclude that the annual rates of return are higher on the big board?

In Excel -- but without using the Data Analysis Toolpack -- calculate the Pooled Variance and the Test Statistic. Then, check your work using the appropriate test from the Data Analysis Toolpack. Be sure to clearly label your results and include an interpretation. Upload the completed spreadsheet showing all your work.

NYSE NASDAQ 15.0 8.8 10.7 6.0 20.2 14.4 18.6 19.0 19.0 17.6 8.7 17.8 17.8 15.9 13.8 17.9 22.7 21.6 14.0 6.0 26.1 11.9 23.4

Explanation / Answer

Data:     

n1 = 11    

n2 = 12    

x1-bar = 16.96    

x2-bar = 15.025    

s1 = 5.14    

s2 = 5.76    

Hypotheses:    

Ho: 1 2    

Ha: 1 > 2    

Decision Rule:    

= 0.01    

Degrees of freedom = 11 + 12 - 2 = 21

Critical t- score = 2.51764801   

Reject Ho if t > 2.51764801   

Test Statistic:    

Pooled SD, s = [{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = (((11 - 1) * 5.14^2 + (12 - 1) * 5.76^2)/(11 + 12 - 2)) = 5.473527634

SE = s * Ö{(1 /n1) + (1 /n2)} = 5.47352763415923 * ((1/11) + (1/12)) = 2.284779363

t = (x1-bar -x2-bar)/SE = (16.96 - 15.025)/2.28477936326831 = 0.84690891

p- value = 0.20329718    

Decision (in terms of the hypotheses):

Since 0.84690891 < 2.517648014 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the annual rates of return are higher on the big board.

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