Federal Gas Tax. The Quinnipiac University Poll conducts nationwide surveys as a public service and for research. In one poll, participants were asked whether they thought eliminating the federal gas tax for the summer months is a good idea. The following problems are based on the results of that poll.

a. Of 611 Republicans, 275 thought it a good idea, and, of 872 Democrats, 366 thought it a good idea. Obtain a 90% confidence interval for the difference between the proportions of Republicans and Democrats who think that eliminating the federal gas tax for the summer months is a good idea.

b. Of 907 women, 417 thought it a good idea, and, of 838 men, 310 thought it a good idea. Obtain a 90% confidence interval for the difference between the percentages of women and men who think that eliminating the federal gas tax for the summer months is a good idea.