---
title: "SDM4 in R: Testing Hypotheses about Proportions (Chapter 19)"
author: "Nicholas Horton (nhorton@amherst.edu)"
date: "June 13, 2018"
output:
pdf_document:
fig_height: 2.8
fig_width: 7
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)
options(digits = 3)
```
```{r, include = FALSE}
# knitr settings to control how R chunks work.
require(knitr)
opts_chunk$set(
tidy = FALSE, # display code as typed
size = "small" # slightly smaller font for code
)
```
## Introduction and background
This document is intended to help describe how to undertake analyses introduced
as examples in the Fourth Edition of *Stats: Data and Models* (2014) by De Veaux, Velleman, and Bock.
More information about the book can be found at http://wps.aw.com/aw_deveaux_stats_series. This
file as well as the associated R Markdown reproducible analysis source file used to create it can be found at http://nhorton.people.amherst.edu/sdm4.
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 19: Testing hypotheses for proportions
### Section 19.1: Hypotheses
We can reproduce the calculation in Figure 19.1 (page 495).
```{r}
sdp <- sqrt(.2*.8/400)
sdp
xpnorm(0.17, mean = 0.20, sd = sdp)
zval <- (0.17 - 0.20)/sdp
zval
pnorm(zval, mean = 0, sd = 1)
```
### Section 19.3: Reasoning of hypothesis testing
The "For Example (page 499)" lays out how to find a p-value for the one proportion z-test.
```{r}
y <- 61
n <- 90
phat <- y/n
phat
nullp <- 0.8
sdp <- sqrt(nullp*(1-nullp)/n)
sdp
onesidep <- xpnorm(phat, mean = nullp, sd = sdp)
onesidep
twosidep <- 2*onesidep
twosidep
```
or we can carry out the exact test (not described by the book):
```{r}
binom.test(y, n, p = nullp)
```