A newsgroup is interested in constructing a 95% confidence interval for the difference in the proportions of Texans and New Yorkers who favor a new Green initiative. Of the 529 randomly selected Texans surveyed, 412 were in favor of the initiative and of the 576 randomly selected New Yorkers surveyed, 473 were in favor of the initiative. a. With 95% confidence the difference in the proportions of Texans and New Yorkers who favor a new Green initiative is between (round to 3 decimal places) and (round to 3 decimal places). b. If many groups of 529 randomly selected Texans and 576 randomly selected New Yorkers were surveyed, then a different confidence interval would be produced from each group. About 95 percent of these confidence intervals will contain the true population proportion of the difference in the proportions of Texans and New Yorkers who favor a new Green initiative and about 5 percent will not contain the true population difference in proportions