Question

1. How do you “pool” two independent samples?
2. What is the minimum number of successes and failures must you have in order to pool the two samples?
3. What is the margin of error for the confidence interval for two proportions?

Answer 1

Solution :

In two sample proportion testing, suppose we have the following statistics;

x1 = number of successes for sample 1;   n1 = sample size for sample 1.

x2 = number of successes for sample 2;   n2 = sample size for sample 2.

And sample proportion fr sample 1 ( ) = x1 / n1;   sample proportion for sample 2 ( ) = x2 / n2.

Then pooled sample proportion is given by the formula;  

In order to pool the two samples for proportion testing these sample should satisfy some conditions as follows;

where n = sample size and p = population proportion

And this should hold for both the samples, sample1 and sample2.

In other words, n*p = number of successes and n*(1-p) = number of failures.

So minimum number of successes and failures for both the samples are 10.

The margin of error fo the confidence interval for two proportions is given by the formula;

where Z(α/2) is the critical value for the confidence interval

and   is the pooled sample proportion.