Question

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?

Answer 1

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