**Answer:**

Now we just take square root on both sides of the interval and we got:

Lower endpoint = 0.2924

Upper endpoint= 0.89995

**Step-by-step explanation:**

**Data given and notation
**

Data: 3.4, 3.1, 3.6, 3.3, 2.7, 2.8, 2.4, 3.6

We can calculate the sample deviation with the following formula:

s=0.442 represent the sample standard deviation

represent the sample mean

n=8 the sample size

Confidence=95% or 0.95

A **confidence interval** is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The **margin of error** is the range of values below and above the sample statistic in a confidence interval.

The **Chi Square distribution** is the distribution of the sum of squared standard normal deviates .

**Calculating the confidence interval
**

The confidence interval for the population variance is given by the following formula:

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a tabel to find the critical values.

The excel commands would be: "=CHISQ.INV(0.025,7)" "=CHISQ.INV(0.975,7)". so for this case the critical values are:

And replacing into the formula for the interval we got:

Now we just take square root on both sides of the interval and we got:

Lower endpoint = 0.2924

Upper endpoint= 0.89995