When we draw one sample s1 from population p and calculate its mean say m1
When we draw another sample s2 from population p and calculate its mean say m2
These two means m1 and m2 will differ slightly from each other because sample mean is dependent on the type of data values which were selected while taking a sample.
Therefore, estimating the population parameter with a point estimate will not be accurate. Hence there is a need for interval estimation. It is where we define some range called as confidence interval which will contain population parameter most of the time.
A confidence interval is a type of estimation which is calculated from the sample data. It defines a range of values for a population parameter (which is unknown). Some confidence level is associated with the confidence interval which tells the probability with which an estimated interval will contain the true value of the population parameter.
You didn’t get it?
No problem!! For the sake of definition we have introduced a quick summary above, but later in this article we will understand it in detail and will jump back to the definition again.
Let us take one example to understand this
Consider that I need to pick up one bus tomorrow to travel from point A to point B, and I need to predict at what time I can get a bus. I can tell something like:
“I am 100% confident that I will get bus tomorrow between 00:01 AM to 23:59 PM”
Confidence level = 100%
Confidence Interval = 00:01 AM to 23:59 PM
Or “I am 95% confident that I will get bus tomorrow between 06:00 AM to 14:00 PM”
Confidence level = 95%
Confidence Interval = 06:00 AM to 14:00 PM
Or “I am 90% confident that I will get bus tomorrow between 08:00 AM to 11:00 AM”
Confidence level = 90%
Confidence Interval = 08:00 AM to 11:00 AM
Or “I am 40% confident that I will get bus tomorrow between 09:00 AM to 09:30 AM”
Confidence level = 40%
Confidence Interval = 09:00 AM to 09:30 AM
At least one thing is clear from the above example:
If you want to be more confident, then your prediction range would be wider. And if your prediction range is narrow, then your confidence will be low.
There can be two scenarios while calculating the confidence intervals.
1) Find the confidence interval when the Standard Deviation of population is given
2) Find the confidence interval when there is no information about the population.