6.27 Public Option, Part III. Exercise 6.13 presents the results of a poll evaluating support for the health care public option plan in 2009. 70% of 819 Democrats and 42% of 783 Independents support the public option.

  1. Calculate a 95% confidence interval for the difference between (pD - pI) and interpret it in this context. We have already checked the conditions for you.

First, calculate the point estimate of the difference in support (pD - pI). Then calculate the standard error, multiply it by Z* (which for 95% Confidence interval is 1.96) and add/subtract this value from the point estimate. This is the confidence interval which is (0.23,0.33).

Answer: (0.23,0.33). This means that our confidence level is 95% that the percentage of Democrats that support the public option are 23% to 33% more than the percentage of Independents who do.

PE <- 0.70-0.42
SE <- sqrt((0.70*(1-0.70)/819) + (0.42*(1-0.42)/783))
z <- 1.96
CI <- z*SE
PE + CI
## [1] 0.3266925
PE - CI
## [1] 0.2333075
  1. True or False: If we 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: TRUE. The confidence interval does not include 0 so the Democrat is indeed more likely to support the public option than the Independent.