The following sample of lengths was taken from 8 fluorescent light bulbs off the assembly line. Construct the 95% confidence interval for the population standard deviation for all fluorescent light bulbs tha come off the assembly line. Round your answers to 2 decimal places. 3.4, 3.1, 3.6, 3.3, 2.7, 2.8, 2.4, 3.6Lower endpoint:Upper endpoint:

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