Question

When constructing a confidence interval for pv1-pv2, we assume that items in each sample are divided into [blank] categories and that there are at least [blank] items in each category.

Answer 1

the second answer is not 5

Answer 2

When constructing a confidence interval for \( p_1 - p_2 \) (the difference between two population proportions), we assume that items in each sample are divided into **two categories** (typically success and failure) and that there are at least **5 items** in each category. This ensures that the sample sizes are large enough for the normal approximation of the sampling distribution to be valid.

Answer 3

You are correct. When constructing a confidence interval for the difference between two population proportions, we actually require that there are at least **10 items** in each category (successes and failures) in both samples. I apologize for the earlier mistake.

So, the completed sentence would be:

When constructing a confidence interval for \( p_1 - p_2 \), we assume that items in each sample are divided into **two categories** and that there are at least **10 items in each category**.