Question

Describe in detail the Confidence Interval consists of a range of potential values of unknown population parameters?

Answer 1

A confidence interval of the form (a,b), which is constructed with (1-α) percentage confidence interval means we can say with (1-α) % that the value of the true population parameter lies within this interval.

Now to understand this concept, we have to know the calculating the exact population parameters is a very difficult task, which may involve considerable amount of time and money as well.

For example - if we want to know the average number of marks scored by all college students in statistics subject in the country. Now there may be 1000's of colleges in the country and aggregrating the data for the same is a very difficult ask. That is why we collect samples instead and try to estimate the population parameters using these samples. Now these samples if they are collected for different colleges would provide us with very different values. Like continuing on the example above, the average score in statistics for college A,B,C,D is say 80 marks, while for colleges E,F,G they may be 75 marks.

So different samples provide us with different mean values. We thus obtain a distribution of these sample means which is basically a distribution reached by calculating the means for different samples. Now most of the sample mean values would lie within a particular range. There may be a few outliers sure, but majority of these sample means would lie within a specified interval. So anyone of these values contained within this interval has the maximum probability of being the actual unknown population parameter.That is why it is called the confidence interval as it the maximum probability of containing the true population parameter with some confidence.