Question

Explain how finding a confidence interval for a population variance is different from finding a confidence interval for a population mean or proportion.

Answer 1

1. (a) Generally, you estimate population mean by using the sample mean Error , this error is the margin error and this whole term Error represents the confidence interval for the population mean.

(b) Now, if you know the standard deviation of the population then, the confidence interval for population mean is given by

.

Where,   is the sample mean, Z is the appropriate Z- score, is the population standard deviation and n is the sample size

2. The confidence interval for the population variance is given by the theorem:

Now, we can see clearly that

1. A confidence interval for the population mean uses a margin of error, which is the distance of the boundaries of the confidence interval to the sample mean. This confidence interval is thus also symmetric about its mean.

2. A confidence interval for the population variance requires no margin of error and is also not symmetric about the sample variance.