--- 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) ```