To conduct a hypothesis test for the difference between two population proportions under independent sampling is,
n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5.
What is population proportion?
In statistics, a population proportion is a parameter that describes a percentage value connected to a population. It is typically denoted by P or the Greek letter π.
As per central limit theorem sample size needs to be greater than 30.
So required conditions are Only if n1 ≥ 30 and n2 ≥ 30.
Also for normal approximation we need the condition
[tex]np \geq 5 and[/tex] n(1 - p) ≥ 5
So one more condition is Only if
n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5
Hence, to conduct a hypothesis test for the difference between two population proportions under independent sampling is
n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5
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