Question

Please, explain to me how can I know when I need to use z- table and when to use t-table distribution. Please, be as detailed as you can. I want to look a problems and know which one I need.

Answer 1

solution:

when sample size is less than 30

and sample standard deviation is given (population standard deviation unknown)

that why we should use t table

example

n = Degrees of freedom = df = n - 1 =15 - 1 = 14

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,14 =: 2.145 ( using student t table)

2.

when sample size greater than 30

amd population standard deviation known

thats why we should use here z table

Population standard deviation =    = 2

Sample size n =65

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )