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.

Democrats

  • p1 = .70
  • n1 = 819

Independents

  • p2 = .42
  • n2 = 783

p1 - p2 = 0.28

95% confidence interval: (0.23, 0.33)

We are 95% confident that the proportion of Democrats who support the plan is 23% to 33% higher than the proportion of Independents who do.

Calculations:

p1 <- 0.70
n1 <- 819
p2 <- 0.42
n2 <- 783

SE <- sqrt((p1*(1-p1))/n1 + (p2*(1-p2))/n2)
SE
## [1] 0.02382271
point_estimate <- p1 - p2
point_estimate 
## [1] 0.28
critical_val_95percent <- 1.96

margin_error <- SE*critical_val_95percent
margin_error
## [1] 0.04669251
CI_95percent <- c(point_estimate - margin_error, point_estimate + margin_error )
CI_95percent
## [1] 0.2333075 0.3266925
  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