Final answer:
To calculate the 90% confidence interval for p1-p2, we use the sample size and number of successes to find the sample proportions and their complements. We then find the error bound and apply it to the sample proportions to form the confidence interval, which reflects our certainty that the interval includes the true difference between population proportions.
Step-by-step explanation:
When constructing a confidence interval for p1-p2, where p1 and p2 are the population proportions, we must first calculate the sample proportions (p') and their respective complements (q'), where p' = x/n and q' = 1 - p'. For the first sample we have p1' = 379/519 and q1' = 1 - p1', and for the second sample p2' = 429/579 and q2' = 1 - p2'. The error bound (EBP) at a 90% confidence level can then be found using the standard error formula for the difference in proportions and looking up the z-value that corresponds to 90% confidence in the standard normal distribution (which would be about 1.645 since it leaves 5% in each tail). Using these values, we can calculate the confidence interval for p1-p2.
A confidence interval gives an estimated range that is likely to include the true population parameter, such as a mean or a proportion, with a specified level of confidence. In this particular study, the 90% confidence interval suggests that, if the study were repeated many times, we would expect the interval to contain the true difference between the two population proportions in 90% of those studies.