Question

the council of higher education wants to compare the percentage of students that score A in two universities. in a random sample of 100 students from university one, 80 received a grade of A; and in a random sample of 160 students from university two, 120 received a grade of A. the 95% confidence interval for the difference in proportion of students who received a grade of A is ???

Answer 1

Solution :

Given that,

n₁ = 100

x₁ = 80

₁ = x₁ / n₁ = 0.8

n₂ =160

x₂ = 120

₂ = x₂ / n₂ = 0.75

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.8 - 0.75

= 0.05

2)

= 1.96 (use z table)

Margin of error =   *

=

= 0.103

3) Required interval is

Point estimate   Margin of error

0.05   0.103

(-0.053 , 0.153)