---
title: "IPS9 in R: Introduction to Inference (Chapter 6)"
author: "Shukry Zablah (szablah20@amherst.edu) and Nicholas Horton (nhorton@amherst.edu)"
date: "July 25, 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 6: Introduction to Inference
This file replicates the analyses from Chapter 6: Introduction to Inference. 

First, load the packages that will be needed for this document: 
```{r load-packages}
library(mosaic)
library(readr)
```

### Section 6.1: Estimating with Confidence 

```{r ex6.1, message=FALSE}
#Fig6.1
Wade <- read_csv("https://nhorton.people.amherst.edu/ips9/data/chapter06/EG06-01WADE.csv")
Wade %>% 
  mutate(North_south = ns,
         East_west = ew) %>%
  gf_point(North_south ~ East_west, data = Wade)
```

### Section 6.2: Tests of Significance

Look at Ex6.17 in page 375. We will recreate the calculation as a function of the vector of observations, the population mean, and the known standard deviation. We then visualize it and get the probability of getting a z score equal or greater. 

```{r ex6.17}
#pg375
z.test <- function(x, mu, sd){
   z = (mean(x) - mu) / (sd / sqrt(length(x)))
   return(z)
}
z <- z.test(x = c(15.84, 15.33, 15.58), mu = 15, sd = 0.25)
xpnorm(z)
```

```{r}
#Ex6.18
z.confint <- function(x, mu, sd) {
  err <- qnorm(0.995)*sd/sqrt(length(x))
  lower <- mean(x) - err
  upper <- mean(x) + err
  return(c(lower, upper))
}

z.confint(x = c(15.84,15.33,15.58), mu = 15, sd = 0.25)
```

### Section 6.3: Use and abuse of tests
### Section 6.4: Power and inference as a decision