Confidence Intervals

Consider a population. You want to calculate the mean expenditure of this population. To do that, you need data of expenditures of all. You cannot really collect this data unless you are a surveillance state.

So, you do a survey and collect expenditures of 50 people (sample size n = 50). How confident are you that the mean expenditure of this sample is the mean expenditure of the population?

Since you cannot be 100% confident, you give a confidence band of mean population.

You don’t know the sampling distribution too! You only did one survey and have one sample. Not a distribution of it. How will you know standard deviation of the sampling distribution now?

Don’t worry. It can be equated to

YOU DON’T KNOW THE POPULATION! THAT’S WHY YOU DID THE SURVEY!

Don’t worry again. It is approximated that the Standard deviation of the population (sigma) is equal to Standard deviation of the sample (S)

But, if you are making this approximations, you cannot use z* any more — especially when the sample size is less (< 30). So, you’ll use — t* — t-Statistics

More on it in future articles!

Life Tip:

If you want to be confident in life, collect more experiences. Increase “n” — sample size. Then you can be more confident of your observations.