At a 005 test a financial advisors claim that the differenc

At a = 0.05, test a financial advisor\'s claim that the difference between the mean dividend rate for listings in the NYSE market and the mean dividend rate for listings in the NASDAQ market is more than 0.75. Assume the two samples are random and independent. NYSE n1=30 x1 = 2.75% Sigma = 1.14% NASDAQ n2 = 50 X2 = 1.6 6% Sigma2 = 0.63%

Solution

Let

u1 = NYSE
u2 = NASDAQ

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0.75  
Ha:   u1 - u2   >   0.75  

At level of significance =    0.05          

As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    2.75          
X2 =    1.66          
              
Calculating the standard deviations of each group,              
              
s1 =    1.14          
s2 =    0.63          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    30          
n2 = sample size of group 2 =    50          

Also, sD =    0.226402297          
              
Thus, the z statistic will be              
              
z = [X1 - X2 - uD]/sD =    1.501751549          
              
where uD = hypothesized difference =    0.75          
              
Now, the critical value for z is              
              
zcrit =        1.645      
              
As z < 1.645, WE FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Thus, there is no significant evidence at 0.05 level that the difference in the mean dividend rate for listings in NYSE and NASDAQ is more than 0.75. [CONCLUSION]