Question

In a class of remedial English that was taught by the lecture method, 52 out of 75 students completed the course with a passing grade. In the same course with computed assistance, 69 out of 95 students passed. At the .05 level, is there a significant difference in the passing rates?

Answer 1

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = Event

p₂: proportion where Sample 2 = Event

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Sample 1	75	52	0.693333
Sample 2	95	69	0.726316

Estimation for Difference

Difference	95% CI for Difference
-0.0329825	(-0.170563, 0.104598)

CI based on normal approximation

Test

Null hypothesis	H₀: p₁ - p₂ = 0
Alternative hypothesis	H₁: p₁ - p₂ ≠ 0

Method	Z-Value	P-Value
Normal approximation	-0.47	0.6385

P-value = 0.6385 is greater than 0.05. So, fail to reject Ho. We can conclude at alpha =0.05 that the proportions are equal.