A newsgroup is interested in constructing a 90% confidence interval for the difference in the proportions of Texans and New Yorkers who favor a new Green initiative. Of the 566 randomly selected...

A newsgroup is interested in constructing a 90% confidence interval for the difference in the proportions of Texans and New Yorkers who favor a new Green initiative. Of the 566 randomly selected Texans surveyed, 400 were in favor of the initiative and of the 542 randomly selected New Yorkers surveyed, 450 were in favor of the initiative.

a.  With 90% 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 566 randomly selected Texans and 542 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.