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 conditions for you.
p.dems <- .70
p.ind <- .42
n.dems <- 819
n.ind <- 783

pt.estimate <- p.dems - p.ind
SE <- sqrt((p.dems*(1-p.dems)/n.dems)+(p.ind*(1-p.ind)/n.ind))
CI.upper <- pt.estimate + SE
CI.lower <- pt.estimate - SE
CI <- c(CI.upper, CI.lower)
CI
## [1] 0.3038227 0.2561773
#our CI is (.31, .26). This tells us that we a 95% confident that the proportion of Democrats who support the plan is between 26 and 31 percent higher than for Independents.
  1. 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.

True: this is supported by our findings above.