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 (P[d] - P[i]) and interpret it in this context. We have already checked conditions for you.

Inputs:

#Democrats
p.1 <- .70
n.1 <- 819

#Independents
p.2 <- .42
n.2 <- 783

Standard Error Calculation:

se <- sqrt((p.1*(1-p.1)/n.1)+(p.2*(1-p.2)/n.2))

Point Estimate Calculation:

pt.est <- p.1 - p.2

Confidence Interval:

ci.upper <- pt.est + se
ci.lower <- pt.est - se
ci <- c(ci.lower, ci.upper)
ci
## [1] 0.2561773 0.3038227
  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. The confidence interval does not include 0. Therefore, it is likely that Democrats support the public option than the Independent.