Assumption of Z-test
- samples are randomly selected from the population
- Population is normally distributed
- population variance is known
Assumption of T-test
- samples are randomly selected from the population
- population is normally distributed
- populations variance is unknown
- sample data are continuous
Z-test VS T-test
- Z test can be only apply when the population variance is known and sample size is 30 or more than 30, and Z-test is used in one population sampling
- T – test only be used population variance is unknown and the sample size is less than 30 and T – test can be used in one population sampling(one sample t- test)and two population sampling. (independent and paired sample t -test)
Independent VS dependent (paired) sample t-test
- independent sample T-test compare variable between two unrelated groups (e.g. – age of the male and female)
- dependent sample T-test compare variable between two related groups ( e.g – body weight before and after the exercise)
Z – test in R
install.packages("TeachingDemos")
library(TeachingDemos)
z.test(x, mu = 0, stdev, alternative = c("two.sided", "less", "greater"),
sd = stdev, n=length(x), conf.level = 0.95)- x = data values
- mu = hypothesized mean
- stdev = standard deviation
- alternative = alternative hypothesis
- conf.level = level of the confident
- n = sample size
T – test in R
1. one sample T -test
install.packages("TeachingDemos")
library(TeachingDemos)
t.test(x, mu, alternative, conf.level, var.equal=TRUE)
- var.equal = the assumption than variable is equal or not
2. Paired (dependent sample t -test)
t.test(x, y, alternative, conf.level, paired = TRUE, var.equal=TRUE)
3. Independent sample T-test
t.test(x, y, alternative, conf.level, paired = FALSE, var.equal=TRUE)
- x = vector of the data values of 1st sample
- y = vector of the data values of 2nd sample
- paired = if samples are dependent or independent