When Student’s T test should be used?
Typically we usually don’t get population standard deviation in real life examples, such that we cannot calculate the standard deviation of population (σ_population) and Z score. So we use Student T test to mitigate this type of problem
Here we will have data like,
μ = Population mean
n= Number of sample
x̄ = Sample mean
α (alpha) = Level of significance = 0.05
σ_ = s = Sample standard deviation (Can be manually calculated with sample data)
We use σ_ = s instead of population standard deviation
Next we calculate t score
t = (x̄ – μ) / σ_sample
σ_sample = s / √n
Degrees of freedom = n-1 (used to look critical value in t table)
Decide on 1 sided test or 2 sided test
We use t-table to get critical value,
- If t < critical value (from table) then accept Null Hypothesis
- If t > critical value (from table) then reject Null Hypothesis
Note: Here we are not using standard normal distribution (with z score), we are using Student’s T distribution w.r.t degrees of freedom
