The correct "independent" condition that must be met to calculate a confidence interval for the difference between two proportions is: "Both samples must be less than 10% of the population they were collected from." Option C
This condition ensures that the samples taken from each population are small relative to the entire population, reducing the potential impact of sampling on the overall population and allowing for the application of statistical inference methods like confidence intervals.
This assumption helps maintain independence and provides validity when making inferences about the population based on the collected samples.
The complete question:
Which of the following is the correct "independent" condition that must be met to calculate a confidence interval for the difference between two proportions?
There is no independent condition for a two proportion z interval.
The sum of the samples must be less than 10% of the combined populations.
Both samples must be less than 10% of the population they were collected from.
You can always assume the samples were collected independently.