one proportion

An ancient pirate coin spent centuries in a treasure chest at the bottom of the sea, and is now a bit gnarly and unbalanced. Can it nevertheless be considered to be a fair coin? To test the idea, students flipped the pirate coin 140 times and it came up heads 83 times.

library(tidyverse)

Compare the pirate coin to a fair coin which has probability \(\pi = 0.5\) of success.

This is a two-sided test because the pirate coin might come up heads too frequently or too infrequently.

hypotheses

\[H_0 : \pi = 0.5\] \[H_0 : \pi \not= 0.5\]

State \(\pi\) and \(\alpha\)

pi <- 0.5
alpha <- 0.05

observed sample statistic

x <- 83        # observed successes
n <- 140       # sample size
(p.hat.observed <- x / n)
## [1] 0.5928571
coin <- data.frame(response = c("head", "tail"),
                   p = c(p.hat.observed, 1 - p.hat.observed))
str(coin)
## 'data.frame':    2 obs. of  2 variables:
##  $ response: Factor w/ 2 levels "head","tail": 1 2
##  $ p       : num  0.593 0.407
ggplot(coin, aes(response, p, fill = response)) +
  geom_bar(stat = "identity") +
  scale_fill_manual(values = c("bisque", "burlywood")) +
  labs(title = "Scissors")