The following sample of weights was taken from 8 muffins off the assembly line. Construct the 90% confidence interval for the population variance for all muffins that come off the assembly line. Round your answers to two decimal places. 12.9,12.5,13.0,13.1,12.3,12.9,12.2, 13.2

And rounded we got:

Step-by-step explanation:

Data given and notation

s represent the sample standard deviation

represent the sample mean

n=8 the sample size

Confidence=90% or 0.90

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:

On this case we need to find the sample standard deviation with the following formula:

The sample mean obtained on this case is and the deviation s=0.378

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

Since the Confidence is 0.90 or 90%, the value of and , and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.05,7)" "=CHISQ.INV(0.95,7)". so for this case the critical values are:

And replacing into the formula for the interval we got:

And rounded we got: