Chisquare distribution give an example of a situation where

Chi-square distribution. give an example of a situation where the variance would need to be controlled.

Solution

For finding confidence interval for variances or std deviation chi square distribution is used.

The population variance formula, when used on a sample, does not give an unbiased estimate of the population variance. In fact, it tends to underestimate the actual population variance. For that reason, there are two formulas for variance, one for a population and one for a sample. The sample variance formula is an unbiased estimator of the population variance. (Unfortunately, the sample standard deviation is still a biased estimator.)

Also, both variance and standard deviation are nonnegative numbers. Since neither can take on a negative value, the domain of the probability distribution for either one is not (,), thus the normal distribution cannot be the distribution of a variance or a standard deviation. The correct PDF must have a domain of [0,). It can be shown that if the original population of data is normally distributed, then the expression (n1)s22 has a chi-square distribution with n1 degrees of freedom.

we will have the inequality 21/2(n1)s222/2. Solving this inequality for the population variance 2, and then the population standard deviation , leads us to the following pair of confidence intervals.

Thus for controlling variance only chi square distribution can help