Arandom sample of 9 wheels of cheese yielded the following weights in pounds has a sample mean of 20.90 and a sample variance of 3.45. assume the weights of wheels of cheese have a normal distribution. find a 90% confidence interval for the population variance.

Step-by-step explanation:

1) Data given and notation

s represent the sample standard deviation

represent the sample variance

n=9 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 .

2) 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 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(0.05,8)" "=CHISQ.INV(0.95,8)". so for this case the critical values are:

And replacing into the formula for the interval we got: