spending

reference:
- ISI, exploration 3.4a, p.189

sample statistics

x.bar.observed <- 704
n <- 1039

two CIs for \(\mu\)

\(s = 150\)

s <- 150
point.estimate <- x.bar.observed
multiplier <- 2
se <- s / sqrt(n)
ci <- point.estimate + multiplier * se * c(-1, 1)
ci
## [1] 694.6929 713.3071

\(s = 300\)

s <- 300
se <- s / sqrt(n)
ci <- point.estimate + multiplier * se * c(-1, 1)
ci
## [1] 685.3858 722.6142

impact of sample size

Recall \[CI = point.estimate + multiplier * SE\] \[SE = \frac{s}{\sqrt{n}}\]

example

n.men <- 562
n.women <- 477

Women plan to spend 704 with \(s = 150\).

Calculate a 95% CI for \(\mu\)

point.estimate <- x.bar.observed
multiplier <- 2
s <- 150
se <- s / sqrt(n.women)
ci <- point.estimate + multiplier * se * c(-1, 1)
ci
## [1] 690.2639 717.7361