Two-Proportions Z-Test

A survey revealed the following information on the prevalence of eye disease. Check if the difference in prevalence is statistically significant.

Residence	Eye Disease		Total
	Yes	No
Rural	24	276	300
Urban	15	485	500

$z = \frac{p_1 - p_2}{\sqrt{p_1(1-p_1)/n_1 + p_2(1-p_2)/n_2}}$

n₁: sample size of population 1 = 300
n₂: sample size of population 2 = 500
p₁: sample proportion for population 1 = 24/300
p₂: sample proportion for population 2 = 15/500

$z = \frac{0.08 - 0.03}{\sqrt{0.08(1-0.08)/300 + 0.03(1-0.03)/500}} = 2.87$

Critical z = 1.96 at a 5% confidence interval.
Therefore, z = 2.87 > critical z; the difference in prevalence of eye disease between urban and rural is significant.

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