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Which of the following is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling.a. In every case.b. Only if n1≥30n1≥30 and n2≥30n2≥30.c. Only if n1p⎯⎯1≥5,n1(1−p⎯⎯1)≥5,n1p¯1≥5,n1(1−p¯1)≥5,n2p⎯⎯2≥5n2p¯2≥5 , and n2(1−p⎯⎯2)≥5.n2(1−p¯2)≥5.d. Only if n1p⎯⎯1≥30,n1(1−p⎯⎯1)≥30,n1p¯1≥30,n1(1−p¯1)≥30,n2p2≥30n2p2≥30 and n2(1−p⎯⎯2)≥30.n2(1−p¯2)≥30.

Answer :

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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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