You are testing lifespan of widgets and gadgets . Select 107 widgets and 116 for

Question

You are testing lifespan of widgets and gadgets . Select 107 widgets and 116 for testing. 42 widgets failed and 47 gadgets failed. Conduct a test against hypoth that true rate of failure is the same against hypoth that they are different. What is test statistic?
-0.242 -0.192 0.589 -0.177 -0.951 -0.665 You are testing lifespan of widgets and gadgets . Select 107 widgets and 116 for testing. 42 widgets failed and 47 gadgets failed. Conduct a test against hypoth that true rate of failure is the same against hypoth that they are different. What is test statistic?
-0.242 -0.192 0.589 -0.177 -0.951 -0.665
-0.242 -0.192 0.589 -0.177 -0.951 -0.665

Explanation / Answer

Formulating the hypotheses          
Ho: p1^ - p2^   =   0  
Ha: p1^ - p2^   =/=   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.392523364      
p2 = x2/n2 =    0.405172414      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.065621232      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -0.192758487 = -0.192 [OPTION B]

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