Question

A random sample from a normal population yields the following 25 values:

                       90 87 121 96 106 107 89 107 83 92

                       117 93 98 120 97 109 78 87 99 79

                        104 85 91 107 89

a. Calculate an unbiased estimate of the population variance.

b. Give approximate 99% confidence interval for the population variance.

c. Interpret your results and state any assumptions you made in order to solve the problem. 

 

Answer 1

Solution

a. Calculate an unbiased estimator of (𝝈²)

By previous lesson, we have s² is an unbiased estimator of 𝝈²

By the formula:

b. Give approximate 99% confidence interval for the population variance.

We have:

                                 

Since: 𝑛=25 ,𝑠=11.93 and 𝛼=0.01

Then, we obtained:                𝐼(𝜇)=(𝟕𝟖.𝟏𝟗 ,𝟑𝟔𝟎.𝟑𝟔)

Therefore: 𝑰(𝝈²)=(𝟕𝟖.𝟏𝟗 ,𝟑𝟔𝟎.𝟑𝟔)

c. We are 99% confident that population variance lies in 𝑰(𝝈𝟐).

We can assume that unbiased estimator for population variance of any random sample with finite variance is s².