---
title: "IPS9 in R: Sampling distributions (Chapter 5)"
author: "Margaret Chien and Nicholas Horton (nhorton@amherst.edu)"
date: "November 10, 2018"
output:
pdf_document:
fig_height: 3
fig_width: 5
html_document:
fig_height: 3
fig_width: 5
word_document:
fig_height: 4
fig_width: 6
---
```{r, include = FALSE}
# Don't delete this chunk if you are using the mosaic package
# This loads the mosaic and dplyr packages
require(mosaic)
```
```{r, include = FALSE}
# knitr settings to control how R chunks work.
knitr::opts_chunk$set(
tidy = FALSE, # display code as typed
size = "small" # slightly smaller font for code
)
```
## Introduction and background
These documents are intended to help describe how to undertake analyses introduced
as examples in the Ninth Edition of \emph{Introduction to the Practice of Statistics} (2017) by Moore, McCabe, and Craig.
More information about the book can be found [here](https://macmillanlearning.com/Catalog/product/introductiontothepracticeofstatistics-ninthedition-moore).
The data used in these documents can be found under Data Sets in the [Student Site](https://www.macmillanlearning.com/catalog/studentresources/ips9e?_ga=2.29224888.526668012.1531487989-1209447309.1529940008#). This
file as well as the associated R Markdown reproducible analysis source file used to create it can be found at https://nhorton.people.amherst.edu/ips9/.
This work leverages initiatives undertaken by Project MOSAIC (http://www.mosaic-web.org), an NSF-funded effort to improve the teaching of statistics, calculus, science and computing in the undergraduate curriculum. In particular, we utilize the `mosaic` package, which was written to simplify the use of R for introductory statistics courses. A short summary of the R needed to teach introductory statistics can be found in the mosaic package vignettes (http://cran.r-project.org/web/packages/mosaic). A paper describing the mosaic approach was published in the *R Journal*: https://journal.r-project.org/archive/2017/RJ-2017-024.
## Chapter 5: Sampling Distributions
This file replicates the analyses from Chapter 5: Sampling Distributions.
First, load the packages that will be needed for this document:
```{r load-packages}
library(mosaic)
library(readr)
```
### Section 5.1: Toward Statistical Inference
### Section 5.2: The Sampling Distribution of a Sample Mean
#### Example 5.5: Sample means are approximately Normal
```{r}
Help <- read_csv("https://nhorton.people.amherst.edu/ips9/data/chapter05/EG05-05HELP60.csv")
# Figure 5.6(a), page 294
gf_dhistogram(~ Length, data = Help, binwidth = 12.5, center = 6.25) %>%
gf_labs(x = "Visit lengths (minutes)", y = "Percent of Visits")
# Figure 5.6(b)
set.seed(124)
HelpSamples <- do(500) * mean(~ Length, data = resample(Help, size = 60))
gf_dhistogram(~ mean, data = HelpSamples, binwidth = 12.5) %>%
gf_labs(x = "Mean length of 60 visits (minutes)", y = "Percent of all means")
# Figure 5.7
gf_qq(~ mean, data = HelpSamples) %>%
gf_labs(x = "Normal Score", y = "Sample mean visit length (minutes)")
```
### Section 5.3: Sampling Distributions for Counts and Proportions