Do teachers find their work rewarding and satisfying The art

Do teachers find their work rewarding and satisfying The article \"Work-Related Attitudes\" (Psychological Reports, 1991: 443-450) reports the results of a survey of 395 elementary school teachers and 266 high school teachers. Of the elementary school teachers, 224 said they were very satisfied with their jobs, whereas 126 of the high school teachers were very satisfied with their work. We are interested to know the difference between the proportion of all elementary school teachers who are very satisfied and all high school teachers who are very satisfied by calculating. Construct a 95% confidence interval for the difference between the proportion of elementary school teachers and high school teachers who are satisfied with their jobs. Based on this confidence interval can you conclude that there is a difference between the proportions Run a (two-sided) hypothesis test with alpha =0.05. Give the test statistic, p-value and conclusion.

Solution

A. Confidence Interval for Diffrence of Proportion

CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
No. of chances( X1 )=224
No.Of Observed (n1)=395
P1= X1/n1=0.567
Proportion 2
No. of chances(X2)=126
No.Of Observed (n2)=266
P2= X2/n2=0.474
C.I = (0.567-0.474) ±Z a/2 * Sqrt( (0.567*0.433/395) + (0.474*0.526/266) )
=(0.567-0.474) ± 1.96* Sqrt(0.002)
=0.093-0.077,0.093+0.077
=[0.016,0.171]

B.
Null, There Is No Significance between them Ho: p1 = p2
Alternate, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =224, n1 =395, P1= X1/n1=0.567
Sample 2 : X2 =126, n2 =266, P2= X2/n2=0.474
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.53
Q^ Value For Proportion= 1-P^=0.47
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.567-0.474)/Sqrt((0.53*0.47(1/395+1/266))
Zo =2.359
| Zo | =2.359
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.359 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 2.3594 ) = 0.0183
Hence Value of P0.05 > 0.0183,Here we Reject Ho