Final answer:
When constructing a confidence interval for a difference between two population proportions, it is important to have at least 10 successes and failures in each sample. This ensures that the assumption of an approximately normal sampling distribution is met.
Step-by-step explanation:
When constructing a confidence interval for a difference between two population proportions, it is important to check that the number of successes and failures in each sample is at least 10. This is because the construction of the confidence interval relies on the assumption that the sampling distribution of the difference between proportions is approximately normal.
In order to meet this assumption, the number of successes and failures should be sufficient to ensure that the sampling distribution is not skewed or heavily influenced by extreme values. If the number of successes and failures in each sample is at least 10, then the sampling distribution can be considered approximately normal, allowing us to construct accurate confidence intervals. It is recommended to have at least 10 successes and 10 failures in each sample to ensure the validity of the confidence interval.