president in 1996

references:
- ISI, exploration 3.5a, p.197
- Literary Digest, Wikipedia

observed statistics in 1996

x <- 1783
n <- 2613
p.hat.observed <- x / n
p.hat.observed
## [1] 0.6823574

99% CI for \(\pi\)

point.estimate <- p.hat.observed
multiplier <- 2
se <- sqrt(p.hat.observed * (1 - p.hat.observed) / n)
se
## [1] 0.009107635
ci <- point.estimate + multiplier * se * c(-1, 1)
ci
## [1] 0.6641422 0.7005727

actually voted

p.actual <- 0.490

how likely is the actual vote given the confidence interval?

Note: We are comparing the actual vote with people describing how they will vote.

z <- (p.actual - point.estimate) / se
z
## [1] -21.12046

president in 1936

observed statistics in 1936

n.surveyed <- 1e7
n.responses <- 2.4 * 1e6
p.hat.observed <- 0.57
p.hat.observed
## [1] 0.57

99% CI for \(\pi\)

point.estimate <- p.hat.observed
multiplier <- 2
se <- sqrt(p.hat.observed * (1 - p.hat.observed) / n.responses)
se
## [1] 0.00031957
ci <- point.estimate + multiplier * se * c(-1, 1)
ci
## [1] 0.5693609 0.5706391

actually voted for Alf Landon

p.actual <- 0.365

how likely is the actual vote given the confidence interval?

Note: We are comparing the actual vote with people describing how they will vote.

z <- (p.actual - point.estimate) / se
z
## [1] -641.487