21 Teach for America Several programs attempt to address th

21. Teach for America - Several programs attempt to address the shortage of qualified teachers by placing uncertified instructors in schools with acute needs—often inner cities. A 1999–2000 study compared students taught by certified teachers with others taught by under certified teachers in the same schools. Reading scores of the students of certified teachers averaged 35.62 points with standard deviation 9.31. The scores of students instructed by under certified teachers had mean 32.48points with standard deviation 9.43 points on the same test. There were 44 students in each group. The appropriate t procedure has 86 degrees of freedom. Is there evidence of lower scores with uncertified teachers? Discuss.

Solution

Set Up Hypothesis
Null, Ho: u1 = u2
Alternate - H1: u1 > u2
Test Statistic
X(Mean)=35.62
Standard Deviation(s.d1)=9.31 ; Number(n1)=44
Y(Mean)=32.48
Standard Deviation(s.d2)=9.43; Number(n2)=44
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =35.62-32.48/Sqrt((86.6761/44)+(88.9249/44))
to =1.57
| to | =1.57
Critical Value
The Value of |t | with (n1+n2-2) i.e 86 d.f is 1.663
We got |to| = 1.57 & | t | = 1.663
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value:Right Tail -Ha : ( P > 1.5718 ) = 0.06167
Hence Value of P0.05 < 0.06167,Here We Do not Reject Ho

We don\'t have evidence of lower sccores with uncertified teachers