P distribution

Relationship between P distribution and Z (standard normal ) distribution

Fig 1 : p distributions are shorter and flatter than z distribution

Fig 2 : As degree of freedom df increases with the sample size, p distribution tend to grow to match z distribution, matching most at df = 30

When you do not know the Standard deviation σ of the population, t distribution is most useful in Hypothesis testing. Using this you can estimate the σ of the entire population from the mean of the sample.

Selecting z and t table