# How to perform z-test and t-test using R? Explain with an example

To perform z- test, let us take data first.

############## 1 sample z test ##########

Fabric

Here fabric is the dataset

Now to perform Normality test, we can perform Anderson-Darling Test which is the following

##### Normality Test##################

library(nortest)

Here Anderson Darling test can be performed by reading a library nortest.

########### 1 sample z-test ##########

Let us perform two sided test which is 1 sample z-test

z.test(fabric\$Fabric_length, alternative = "two.sided", mu = 0, sigma.x = 4,

sigma.y = NULL, conf.level = 0.95)

############## 1 sample t test ##########

Now we will be performing t-test in another dataset called bolt_d which contains diameter of bolts.

##### Normality Test##################

library(nortest)

########### 1 sample t-test ##########

To perform 1 sample t-test, we can do the following

t.test(bolt_d\$Diameter, mu = 0, alternative = "two.sided")

############2 sample T Test ##################

attach(Promotion)

colnames(Promotion)<-c("Credit","Promotion.Type","InterestRateWaiver","StandardPromotion")

# Changing column names

View(Promotion)

attach(Promotion)

#############Normality test###############

shapiro.test(InterestRateWaiver)

# p-value = 0.2246 >0.05 so p high null fly => It follows normal distribution

shapiro.test(StandardPromotion)

# p-value = 0.1916 >0.05 so p high null fly => It follows normal distribution

#############Variance test###############

var.test(InterestRateWaiver,StandardPromotion)#variance test

# p-value = 0.653 > 0.05 so p high null fly => Equal variances

############2 sample T Test ##################

t.test(InterestRateWaiver,StandardPromotion,alternative = "two.sided",conf.level = 0.95,correct = TRUE)#two sample T.Test

# alternative = "two.sided" means we are checking for equal and unequal

# means

# null Hypothesis -> Equal means

# Alternate Hypothesis -> Unequal Hypothesis

# p-value = 0.02523 < 0>

# unequal means

?t.test

t.test(InterestRateWaiver,StandardPromotion,alternative = "greater",var.equal = T)

# alternative = "greater means true difference is greater than 0

# Null Hypothesis -> (InterestRateWaiver-StandardPromotion) < 0>

# Alternative Hypothesis -> (StandardPromotion - InterestRateWaiver) > 0

# p-value = 0.01211 < 0> p low null go => accept alternate hypothesis

# InterestRateWaiver better promotion than StandardPromotion