Experiments, Data and Conclusions: The Lady and the Tea

UNG MATH 3350 (online)

I. Initialization Block

Initializing RStudio

The Mosaic package was created by statistics instructors to help students learn the coding in R. Commands are streamlined to be more intuitive. Execute the code block below to load Mosaic (required each session).

library(mosaic)

II. Exercises

1. Using the Mosaic function rflip, flip 16 coins and count the number of Heads. Repeat 10,000 times using the Mosaic function do. Estimate the probability that, if Dr. Bristol tasted 16 cups of tea each of which was randomly chosen to be “tea first” or “milk first,” that she would get at least 14 correct using a histogram with the type parameter set to “count.”

2. Find the theoretical probability in Exercise 1 by altering the code block that created the pFun function. Use your new pFun function and R’s sum function for the calculations. How does your theoretical calculation compare to your empirical estimate in Exercise 1?

pFun <- function(t) {
  choose(16,t)*(.5)^t *(.5)^(16-t)
}

3. For 32 coins flips (and 10,000 randomized draws), estimate the probability that Dr. Bristol would get at least 24 correct if she were guessing at random. Use a histogram with the type parameter set to “count.” Update pFun to find the theoretical probabilities and compare the two results.

4. How many successes out of 100 would Dr. Bristol need to have before you would believe she was not guessing at random? Explain your reasoning based on empirical or theoretical calculations.

III. Code Blocks

rflip(8)

coins = do(10000) * rflip(8)
tally(~ heads, data = coins)

histogram(~heads, data = coins,
          width = 1,
          type = "count")

choose(8,7)*.5^7*.5^1

# Creating Function
pFun <- function(t) {
  choose(8,t)*(.5)^t *(.5)^(8-t)
}
# Creating T-chart ()
x = 0:8
tChart = data.frame(x,pFun(x))
names(tChart) = c("x","p(x)")
print(tChart)

pFun(7)+pFun(8)

sum(pFun(7:8))