Question

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 575 randomly selected Texans surveyed, 396 were in favor of the initiative and of the 564 randomly selected New Yorkers surveyed, 452 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  (round to 2 decimal places).

b. If many groups of 575 randomly selected Texans and 564 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.

Answer 1

The solution to this problem is given by