Do teachers find their work rewarding and satisfying An arti

Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 398 elementary school teachers and 262 high school teachers. Of the elementary school teachers, 221 said they were very satisfied with their jobs, whereas 124 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 p_elementary ? p_{high school}. Round your answers to four decimal places.)

Solution

CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
No. of chances( X1 )=221
No.Of Observed (n1)=398
P1= X1/n1=0.5553
Proportion 2
No. of chances(X2)=124
No.Of Observed (n2)=262
P2= X2/n2=0.4733
C.I = (0.5553-0.4733) ±Z a/2 * Sqrt( (0.5553*0.4447/398) + (0.4733*0.5267/262) )
=(0.5553-0.4733) ± 1.96* Sqrt(0.0016)
=0.082-0.0777,0.082+0.0777
=[0.0043,0.1597]