# Lesson 12—The Chi-Square Test for Goodness of Fit

#### By Olivia Mah

First published on April 20, 2019

### Learning Objectives

Perform a chi-square goodness-of-fit test.

### Demonstration

Goal: To conduct a chi-square goodness-of-test for #21.24 in our textbook.

For #21.24, the null hypothesis is:

$$H_0: p_{tall} = 0.75, p_{dwarf} = 0.25$$

Here is the R code:

chisq.test(c(787, 277), p=c(0.75, 0.25))



Explanation:

We use the R function chisq.test to run a chi-square test.

The arguments for the chisq.test function are:

c(787, 277) is the vector that stores the two observed values

p=c(0.75, 0.25) is the vector that stores the probabilities in the theoretical model (ratio 3:1).  (We must use the letter p but not any other letters in this chisq.test function).

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