---
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