Sampling Distributions

library(tidyverse)
library(openintro)

download.file("http://www.openintro.org/stat/data/ames.RData", destfile = "ames.RData")
load("ames.RData")

Exercise 1

This population distribution has a strong left skew with a deep right tail. This represents that most home greater living areas are around 1500 square feet, while some very large areas can reach up to 6000 square feet.

# Insert code for Exercise 2 here
area <- ames$Gr.Liv.Area
price <- ames$SalePrice
samp1 <- sample(area, 50)
summary(samp1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     630    1067    1402    1418    1682    2728

hist(samp1)

Exercise 2

My sample population has a mean slightly above the total population mean of 1499. My sample mean was 5% above the total population mean. This standard error could be considered acceptable, especially since it was randomly pulled from the total population dataset.

# Insert code for Exercise 2 here
mean(samp1)

## [1] 1417.84

Exercise 3

My second sample mean was 1456, slightly below the total population mean. This aligns with central limit theorum, with one sample slightly above and one sample slightly below the total mean. Taking larger samples of 100 and 1000 would begin generating sample means closer to the total mean, with a larger dataset representing more of the population with each repetition.

# Insert code for Exercise 3 here
samp2 <- sample(area, 50)
mean(samp2)

## [1] 1418.8

sample_means50 <- rep(NA, 5000)

for(i in 1:5000){
   samp <- sample(area, 50)
   sample_means50[i] <- mean(samp)
   }

hist(sample_means50)

hist(sample_means50, breaks = 25)

Exercise 4

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# Insert code for Exercise 4 here

Exercise 5

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# Insert code for Exercise 5 here

Exercise 6

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# Insert code for Exercise 6 here