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For differences of sampled proportions, explain the circumstances for which a) one uses the two proportions...

For differences of sampled proportions, explain the circumstances for which a) one uses the two proportions pz and p2 to calculate the SE; b) or uses the pooled proportion to calculate the SE.

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Answer #1

For Hypothesis Testing of difference in two proportions:

If the hypothesis testing is as follows:

H0: Null Hypothesis: p1 - p2 = 0

HA: Alternative Hypothesis: p1 - p2 0,

we use the pooled proportion to calculate the SE.

i.e.,

If the Hypothesis involves testing of difference other than 0, then unpooled proportion to calculate the SE will be used.

For example:

If the hypothesis testing is as follows:

H0: Null Hypothesis: p1 - p2 = 0.1

HA: Alternative Hypothesis: p1 - p2 0,1

we use the unpooled proportion to calculate the SE.

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