Question

A charter school system sets a standard for their schools’ graduation and retention rates in order for those schools to receive a certain amount of funding. Suppose the graduation rate established by the school system is a minimum of 67% in order for the schools to receive priority funding the following academic year. One of the schools is concerned that their graduation rate may be too low. Assume that at this particular school, only 300 of its 498 students are expected to graduate. 

A) Is it appropriate in this instance, based on the data provided, for a normal approximation to be made?

B) Conduct a formal test to determine if there is a significant difference between the graduation rate at the particular school and the standard set by the school system. Use an alpha level of 0.05.

Answer 1

A)

np= 498 * 0.67 = 333.66 >= 5

n(1-p) = 498 * ( 1 - 0.67) = 164.34 >= 5

Since both success and failure conditions are satisfied,

the normal approximation can be appropriate.

B)

H0: p = 0.67

Ha: p 0.67

= X / n = 300/498 = 0.6024
Test Statistic :-
Z = ( - p ) / ( ?((p ( 1 - p) )/n)
Z = ( 0.6024 - 0.67 ) / ( ?(( 0.67 * 0.33) /498))
Z = -3.21

Test Criteria :-
Reject null hypothesis if Z < -Z(?/2)
Z(?/2) = Z(0.05/2) = 1.96
Z < -Z(?/2) = -3.21 < -1.96, hence we reject the null hypothesis
Conclusion :- We Reject H0

 

We have sufficient evidence to conclude that there is significant difference between graduation rate at particular school and standard set by the school system.