The state of Georgia's HOPE scholarship program guarantees fully paid tuition to Georgia public universities for Georgia high school seniors who have a B average in academic requirements as long as they maintain a B average in college. It was reported that 28.3% of a random sample of 137 students entering Ivan Allen College at Georgia Tech (Social Science and Humanities) with a HOPE scholarship lost the scholarship at the end of the first year because they had a GPA of less than 3.0. It was also reported that 22 of a random sample of 111 students entering the College of Computing with a B average had lost their HOPE scholarship by the end of the first year. Required:
Is there evidence that the proportion who lose HOPE scholarships is different for the College of Computing than for the Ivan Allen College?

We accept H₀    p₁  =  p₂  : We don´t have evidence to support any difference between the proportions

Step-by-step explanation:

Information from Ivan Allen College;

Sample size  n₁  = 137

The proportion of students failing

p₁  =  0,283      q₁ =  1  -  p₁     q₁  =  1  -  0,283    q₁ =  0,717

Information from College of Computing:

Sample size   n₂  =  111

x₂  ( number of students failing )  =  22

The proportion of students failing

p₂  =  0,1981      q₂  =  1  -  0,1981     q₂  =  0,8019

Hypothesis Test:

Null Hypothesis:                             H₀          p₁  =  p₂

Alternative Hypothesis                  Hₐ          p₁  ≠  p₂

Alternative Hypothesis indicates the test is a two-tail test

Choosing a significance level   α  =  0,05   ( Confidence Interval 95%)

we get from z table   z(c)  = 1,64

To obtain z(s)

z(s)  =  (  p₁ -  p₂  ) / EED

EED = √(p₁*q₁)/n₁  +  p₂*q₂)/n₂

EED = √ (0,283*0,717)/137   +  ( 0,1981*0,8019)/111

EED = √  0,00148  +  0,00143

EED = 0,054

And

z(s)  = ( 0,283 -  0,1981 )/ 0,054

z(s) = 1,57

Comparing   z(c)  and  z(s)

z(c) > z(s)

Then z(s) is in the acceptance region for H₀ : We accept H₀