8.7 : Estimating Population Standard Deviation

Sample statistics are often used to estimate  population parameters. For instance,  the sample standard deviation can reasonably estimate the population standard deviation if n is sufficiently large.

But, the sample standard deviation often underestimates or overestimates the population standard deviation. So, confidence intervals are determined to compensate for these biases.

It's important to note that only randomly selected samples from a normally distributed population can be used to estimate  population parameters.

Consider the data on temperature variations with a sample standard deviation of 1.5 degrees Celsius. Using this, one can estimate the population standard deviation with a suitable confidence interval, say 95%.

First, using the chi-square table, find the right and left critical values. Then determine the confidence intervals of the population variance, separately for the left and the right critical values.

Taking the square root of these values gives the confidence intervals of the population standard deviation, which can be rounded off for convenience.

So, one can say with 95% confidence that the true value of the population standard deviation lies between 1.03 and 2.74 degrees Celsius.