In a small town of 5,832 people, the mayor wants to determine if there is a difference in the proportion of voters ages 18–30 who would support an increase in the food tax, and the proportion of voters ages 31–40 who would support an increase in the food tax. An assistant to the mayor surveys 85 randomly chosen voters ages 18–30, and finds that 62 support the increase. A random sample of 70 voters ages 31–40 is also surveyed, and 56 support the increase. Assuming the conditions for inference have been met, what is the 99% confidence interval for the difference in proportions of voters who would support the increase in the food tax for the different age groups?
(0.27 minus 0.20) plus-or-minus 1.96 StartRoot StartFraction 0.27 (1 minus 0.27) Over 85 EndFraction + StartFraction 0.20 (1 minus 0.20) Over 70 EndFraction EndRoot
(0.73 minus 0.80) plus-or-minus 1.96 StartRoot StartFraction 0.73 (1 minus 0.73) Over 70 EndFraction + StartFraction 0.80 (1 minus 0.80) Over 85 EndFraction EndRoot
(0.27 minus 0.20) plus-or-minus 2.58 StartRoot StartFraction 0.27 (1 minus 0.27) Over 70 EndFraction + StartFraction 0.20 (1 minus 0.20) Over 85 EndFraction EndRoot
(0.73 minus 0.80) plus-or-minus 2.58 StartRoot StartFraction 0.73 (1 minus 0.73) Over 85 EndFraction + StartFraction 0.80 (1 minus 0.80) Over 70 EndFraction EndRoot