Confidence Interval in Statistics | Confidence Interval formula | Confidence Interval example

0:01 This short animated video explains the concept of "Confidence Interval" and how to construct 95% and 99% confidence interval with help of examples So don't go anywhere else just sit back and enjoy this video Before we understand Confidence Interval let us first understand what do we mean by estimate ? Everyone makes some kinds of estimates at some point of time in their life Suppose when are crossing the road, you estimate the speed of the car that is approaching you Based on estimate you decide whether to Wait, Walk or Run.

0:55 Let’s look at the estimate in the Statistical term It gives you some facts about how the population could be We can have two types of estimates about the population Point estimate and Interval estimate Lets us first look at point estimate So point estimate is a single value or a number that is used to estimate of a population parameter Lets take an example. Assume that this is the population and we draw a sample out of it using any sampling technique

1:44 So we pick 4 people from this lot and we take their average weight of these 4 samples which is coming around as 60Kg 60 Kg is a single point estimate of population mean Point estimate is often insufficient because its either Wrong or Right. Assuming that we know we are wrong here and assuming that we off target by 5kg That means whaever we have expected is a good estimate But if we are off we are off target by 20 or 30 kg, then that is not the right estimate Also the point estimate is going to be different from the

2:32 population parameter due to some samling error There is no way to know who close it is to the actual parameter For this reason, statisticians like to give an interval estimate which gives them some range of values used to estimate the parameter Sample mean is a point estimate of Population mean Now let us understand the Interval Estimates Interval Estimate is a Range of values used to estimate an unknown population parameters. It gives you the estimates that what is the range of values by calculating two values or intervals UCL and LCL within which a parameter is expected to lie. Interval estimates of population parameters are

3:21 called confidence intervals. And statisticians prefer interval estimates because interval estimates are accompanied by a statement concerning the degree of confidence that the interval contains the population parameter being estimated Confidence interval which is the most common type of interval estimate is made of two elements One is the Point estimate and other is Margin of Error Point estimate +/- Margin of Error It indicates the error in two ways one by the extent of its range and other by probability of true population parameter lying within the range

4:14 Confidence intervals are often confusing When we construct a confidence interval we are estimating a population parameter based on the data from a sample So 95% confidence interval is a range of values that you can be 95% certain or confident contains the true mean of the population The correct interpretation of a 95% confidence interval is that "We are 95% confident that the population parameter is between 50 and 70." Lets us understnd this with help of an example Example 1 : Confidence Interval for Single population Mean

6:26 Example 2 : Confidence Interval for Single population proportion

7:49 So we are 99 % confident that true proportion of billing statement that contains errors would li between 7.7 % and 12.7%