Japanese managers are perhaps more motivated than American m

\"Japanese managers are perhaps more motivated than American managers\". A randomly selected group of each were administered by the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL results are summarized below. Use alpha =0.05 to test the claim, (setup the hypotheses, the test value, and the statistical decision and conclusion) Compute the test p-value.

Solution

1.

Let

u1 = japanese mean
u2 = american mean

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  
At level of significance =    0.05          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    68.25          
X2 =    66          
              
Calculating the standard deviations of each group,              
              
s1 =    7          
s2 =    11          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    100          
n2 = sample size of group 2 =    210          

Also, sD =    1.032564999          
              
Thus, the z statistic will be              
              
z = [X1 - X2 - uD]/sD =    2.179039579          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
zcrit =        1.645      
              
As z > 1.645,   WE REJECT THE NULL HYPOTHESIS.          
Thus, there is significant evidnece that Japanese managers are more motivated than American managers at 0.05 level. [CONCLUSION]

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2.

              
Also, using p values, as this is 1 tailed,              
              
p =    0.01504317   [ANSWER]