chi_square

###install.packages("infer")
###install.packages("openintro")

library(tidyverse)

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library(infer)

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library(openintro)

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q170a<-matrix(c(0.2012, 0.2, 0.28465, 0.2,0.183798, 0.2, 0.258921, 0.2, 0.07444, 0.2),ncol=2,byrow=TRUE)
rownames(q170a)<-c("sd","d","n","a", "sa")
colnames(q170a)<-c("observed","expected")
q170a <- as.table(q170a)
q170a

##    observed expected
## sd 0.201200 0.200000
## d  0.284650 0.200000
## n  0.183798 0.200000
## a  0.258921 0.200000
## sa 0.074440 0.200000

null.probs = c(5/25, 5/25, 5/25, 5/25, 5/25)
q170adist = c(2735, 3868, 2498,3519, 971)
chisq.test(q170adist, p=null.probs)

## 
##  Chi-squared test for given probabilities
## 
## data:  q170adist
## X-squared = 1863.3, df = 4, p-value < 2.2e-16