By surveying 5,000 randomly selected factory workers, this institute learned that 785 of them were union members. Similarly, by surveying 3000 randomly selected female factory workers, it learned that 327 of them were unionized. 1. Establish a 99% confidence interval for the difference in proportions between men and women.

2. Does the interval calculated in 1) lead you to believe that the unionization rate varies significantly by gender? Justify your answer.