Question

In order to find confidence interval for population mean~

a) When to use either t distributon or Z confidence interval ...if not mentioned in data?

b)when it is mentioned data is normally distributed

c)when mentioned assume population standard deviation ( not just standard deviation )

pls give me more identification tips if any... I will definitely give a reward.

Answer 1

a) When it is not mentioned in data, then always use Z- distribution when population standard deviation is given and always use t-distribution when population standard deviation is not given.

b) When mentioned data is normally distribution, then also look for population standard deviation , if it is there in the data then use z-distribution and if it is not there then use t-distribution And also when you are dealing with proportions then also use z-distribution.

c) When it is mentioned that assume population standard deviation , then it is clearly giving you the population standard deviation so you will use z-distribution not t -distribution

In short, first of all just look whether there is population standard deviation in the data or not.

If it is there then use z-distribution and if it is not then use t-distribution.