A newsgroup is interested in constructing a 99% confidence interval for the difference in the proportions of Texans and New Yorkers who favor a new Green initiative. Of the 508 randomly selected Texans surveyed, 419 were in favor of the initiative and of the 558 randomly selected New Yorkers surveyed, 451 were in favor of the initiative. a. With 99% confidence the difference in the proportions of Texans and New Yorkers who favor a new Green initiative is between and .
b. If many groups of 508 randomly selected Texans and 558 randomly selected New Yorkers were surveyed, then a different confidence interval would be produced from each group. About 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 percent will not contain the true population difference in proportions.