Confidence Interval

A confidence interval is a sample parameter, used to estimate the value of the population variable. In other words, it is a range of values within which a parameter lies with an associated probability. The degree of certainty that the parameter will lie within the given range is the degree of confidence. The degree of certainty depends on the width of the interval -

> Very narrow interval: very uncertain (1  standard deviation of mean & 68% confidence level)

> Wide interval: much more certain (2 standard deviations  of mean and 95% confidence level)

> Extremely wide interval: nearly perfectly certain (2.5 standard deviations  of mean and 99% confidence level)

> Infinitely wide interval: Absolutely certain.

Example:

To illustrate, let's assume that the average age of members in a club is normally distributed with mean 50 and standard deviation 5. In a normal distribution, the 95% confidence interval is defined as 2 times standard deviation on both sides of the mean, i.e., 40 to 60 years in our case. If the 95% confidence interval is 40 to 60, we can say that if a new member joins, his age will be between 40 and 60 with 95% confidence level or the probability of his age falling in between 40 and 60 years is 95%.