There are 300 welders employed at Maine Shipyards Corporatio

There are 300 welders employed at Maine Shipyards Corporation. A sample of 30 welders revealed that 18 graduated from a registered welding course. Construct the 95 percent confidence interval for the proportion of all welders who graduated from a registered welding course. (Round your answers to 2 decimal places.)

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.6          
              
Also, we get the standard error of p, sp:      
As N = 300, n = 30,      
              
sp = sqrt[p^ (1 - p^) / n]*sqrt[(N-n)/(N-1) =    0.086399554          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.169340014          
lower bound = p^ - z(alpha/2) * sp =   0.430659986          
upper bound = p^ + z(alpha/2) * sp =    0.769340014          
              
Thus, the confidence interval is              
              
(   0.430659986   ,   0.769340014   ) [ANSWER]