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 520 randomly selected Texans surveyed, 420 were in favor of the initiative and of the 534 randomly selected New Yorkers surveyed, 471 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(round to 3 decimal places) and(round to 3 decimal places).

b.If many groups of 520 randomly selected Texans and 534 randomly selected New Yorkers were surveyed, then a different confidence interval would be produced from each group. Aboutpercent 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 aboutpercent will not contain the true population difference in proportions.