Question

A Washington Post article from 2009 reported that "support for a government-run health-care plan to compete with private insurers has rebounded from its summertime lows and wins clear majority support from the public." More specifically, 70 percent of Democrats back the plan, while almost nine in 10 Republicans oppose it. Independents divide 51 percent in favor of and 42 percent against the legislation. 7% responded with "other". There were 811 Democrats, 566 Republicans and 782 Independents surveyed. Round all results to 4 decimal places. a. Calculate a 95% confidence interval for the difference between pDemocrat−pIndependent . We have already checked conditions for you. Lower: Upper: b. True or false: If we had picked a random Democrat and a random Independent at the time of this poll, it is more likely that the Democrat would support the public option than the Independent.

Answer 1

Answer:

Given,

p1 = 70% = 0.7

p2 = 51% = 0.51

n1 = 811

n2 = 782

a)

To give the 95% confidence interval for the difference between pDemocrat−pIndependent

For 95% confidence interval , z value is 1.96

Interval = (p1 - p2) +/- z*sqrt(p1pq/n1 + p2q2/n2)

substitute values

= (0.70 - 0.51) +/- 1.96*sqrt(0.7(1-0.7)/811 + 0.51(1-0.51)/782)

= 0.19 +/- 0.0471

= (0.19 - 0.0471 , 0.19 + 0.0471)

= (0.1429 , 0.2371)

If we had picked a random Democrat and a random Independent at the time of this poll, it is more likely that the Democrat would support the public option than the Independent True.