# Confidence Interval

What is Confidence Interval?

For estimate the unknown population parameters such as a population mean or a population parameter, there are two estimates available. First is the point estimates and second is the interval estimates. To find out the value of a single sample statistic, point estimate is used. But around the point estimate, range of numbers that is interval, confidence interval estimate is constructed. Construction of confidence interval is done such that the probability that the population parameter is located somewhere within the interval is known.

Need of Confidence Interval:

To find out, how accurate is the sample statistic, you need to construct a confidence interval estimate. You can have unknown population parameter, now you calculate a sample statistic of that population by taking an appropriate sample from that population. To check the reliability of that point estimate whether it lies within the population region or not, it is used.

Suppose, you want to estimate the mean CGPA of the PGP students of IIM Raipur of current year. An unknown population mean us denoted by µ as in this case the mean of the CGPA of the IIM Raipur’s students. Now you select a sample of students and calculate the sample mean say 6.2. The sample mean, X = 6.2, is a point estimate of the population mean, µ. But how accurate is 6.2? Confidence interval estimate can give answer to such questions.

Understanding confidence interval:

The sample mean varies from sample to sample because it depends on the items selected in the sample. Developing the interval estimate of the population mean, you need to take the known variability from sample to sample into consideration. Estimation of value of the population parameter should have specified confidence to verify the correctness of estimation. In other words, there is specified confidence that µ is somewhere in the range of numbers defined by the interval.

Suppose you estimate interval of the mean CGPA of students of the IIM Raipur of current year is (6.0 ≤ µ ≥ 6.4) and you can say it with 95% confidence interval. So you can interpret that I am 95% confident that the mean CGPA of IIM Raipur’s PGP students is between 6.0 and 6.4. There is only 5 % chance that the CGPA is below 6.0 or above 6.4.

Suman Gupta_ Section A_13FPM005_Group9