The table below presents the summary statistics for the starting annual salaries

Question

The table below presents the summary statistics for the starting annual salaries (in thousands of dollars for individuals entering the public accounting and financial planning professions. Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning assuming that the two population variances are the same. Suppose sigma = 0.05. Which of the following represents the correct conclusions> The null hypothesis is rejected. The null hypothesis is not rejected. Insufficient information exists on which to make a decision. The alternative hypothesis is rejected.

Explanation / Answer

Data:     

n1 = 12    

n2 = 14    

x1-bar = 59.5    

x2-bar = 58.2    

s1 = 2.25    

s2 = 2.48    

Hypotheses:    

Ho: 1 2    

Ha: 1 > 2    

Decision Rule:    

= 0.05    

Degrees of freedom = 12 + 14 - 2 = 24

Critical t- score = 1.71088207   

Reject Ho if t > 1.71088207   

Test Statistic:    

Pooled SD, s = [{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = (((12 - 1) * 2.25^2 + (14 - 1) * 2.48^2)/(12 + 14 - 2)) = 2.377347086

SE = s * {(1 /n1) + (1 /n2)} = 2.37734708586413 * ((1/12) + (1/14)) = 0.935243342

t = (x1-bar -x2-bar)/SE = (59.5 - 58.2)/0.935243342198694 = 1.390012568

p- value = 0.08864207    

Decision (in terms of the hypotheses):

Since 1.39001257 < 1.710882067 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that 1 > 2   

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