T Test

library(readxl)

## Warning: package 'readxl' was built under R version 4.1.3

bmi <- read_excel("C:/Users/Lab pc/Downloads/bmi.xlsx")
View(bmi)

attach(bmi)
names(bmi)

## [1] "BMI"    "Height" "Weight" "Gender"

#Ho : mu<8 + 95% confidence interval
t.test(BMI, mu = 20,alternative="two.side",conf.level =0.95)

## 
##  One Sample t-test
## 
## data:  BMI
## t = 0.80547, df = 9, p-value = 0.4413
## alternative hypothesis: true mean is not equal to 20
## 95 percent confidence interval:
##  18.71598 22.70402
## sample estimates:
## mean of x 
##     20.71

boxplot(BMI ~ Gender)

#Ho : BMI OF MALE = BMI OF FEMALE
#assumption - non-equal variances

t.test(BMI ~ Gender, mu=0, alt="two.sided", paired=F, conf.level=0.95)

## 
##  Welch Two Sample t-test
## 
## data:  BMI by Gender
## t = -2.143, df = 7.5951, p-value = 0.06629
## alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
## 95 percent confidence interval:
##  -6.2063093  0.2563093
## sample estimates:
## mean in group Female   mean in group Male 
##               18.925               21.900

#By default values which t.test takes are mention in the above line
t.test(BMI ~ Gender)

## 
##  Welch Two Sample t-test
## 
## data:  BMI by Gender
## t = -2.143, df = 7.5951, p-value = 0.06629
## alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
## 95 percent confidence interval:
##  -6.2063093  0.2563093
## sample estimates:
## mean in group Female   mean in group Male 
##               18.925               21.900

t.test(BMI[Gender=='Male'],BMI[Gender=='Female'])

## 
##  Welch Two Sample t-test
## 
## data:  BMI[Gender == "Male"] and BMI[Gender == "Female"]
## t = 2.143, df = 7.5951, p-value = 0.06629
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.2563093  6.2063093
## sample estimates:
## mean of x mean of y 
##    21.900    18.925