Chi square test

##Chi Square test
library(readxl)

## Warning: package 'readxl' was built under R version 3.5.2

Bahaman <- read_excel(file.choose()) # Bahaman.xls
View(Bahaman)
attach(Bahaman)
table(Country, Defective)

##             Defective
## Country        0   1
##   Bangladesh 183  17
##   China      179  21
##   India      175  25
##   Srilanka   178  22

chisq.test(table(Country,Defective))

## 
##  Pearson's Chi-squared test
## 
## data:  table(Country, Defective)
## X-squared = 1.7244, df = 3, p-value = 0.6315

# P - value = 0.6315 > 0.05 => accept null hypothesis
# => All countries have equal proportions

Proportinal T test

Johnytalkers <- read_excel(file.choose())
View(Johnytalkers)
attach(Johnytalkers)
table(Icecream,Person)

##                   Person
## Icecream           Adults Children
##   Did Not Purchase    422      588
##   Purchased            58      152

table1 <- table(Icecream,Person)
View(table1)
table1

##                   Person
## Icecream           Adults Children
##   Did Not Purchase    422      588
##   Purchased            58      152

prop.test(x=c(58,152),n=c(480,740),conf.level = 0.95,correct = FALSE,alternative = "two.side")

## 
##  2-sample test for equality of proportions without continuity
##  correction
## 
## data:  c(58, 152) out of c(480, 740)
## X-squared = 14.613, df = 1, p-value = 0.000132
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.1257722 -0.0433719
## sample estimates:
##    prop 1    prop 2 
## 0.1208333 0.2054054

prop.test(x=c(58,152),n=c(480,740),conf.level = 0.95,correct = FALSE,alternative = "less")

## 
##  2-sample test for equality of proportions without continuity
##  correction
## 
## data:  c(58, 152) out of c(480, 740)
## X-squared = 14.613, df = 1, p-value = 6.599e-05
## alternative hypothesis: less
## 95 percent confidence interval:
##  -1.0000000 -0.0499958
## sample estimates:
##    prop 1    prop 2 
## 0.1208333 0.2054054

#two.sided -> means checking for equal proportions of adults and childern under purchased
# p-value = 6.261e-05 < 0.05 accept alternative hypothesis i.e.
# unequal proportions
# Ha -> proportions of Adults > Porportions of children
# H0 -> Proportions of childeren > Proportions of adults
# p-value = 0.999 > 0.05 accept null hypothesis
# so proportion of childern > proportion of children
# Do not launch the ice cream shop