Do teachers find their work rewarding and satisfying? An article reports the res

Question

Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 394 elementary school teachers and 266 high school teachers. Of the elementary school teachers, 227 said they were very satisfied with their jobs, whereas 121 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI. (Use pelementary phigh school. Round your answers to four decimal places.)

( _______ , _______ )

Explanation / Answer

Getting p1^ and p2^,          
          
p1^ = x1/n1 = 227/394 =   0.576142132      
p2 = x2/n2 = 121/266 =   0.454887218      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.039395452      
          
          
For the   95%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.025      
z(alpha/2) =    1.959963985      
Margin of error = z(alpha/2)*sd =    0.077213667      
lower bound = p1^ - p2^ - z(alpha/2) * sd =    0.044041247      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.198468581      
          
Thus, the confidence interval is          
          
(   0.044041247   ,   0.198468581 ) [ANSWER]

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