Answer:
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:
![s=sqrt{\frac{\sum_{i=1}^9 (x_i -\bar x)^2}{n-1}} The sample variance given was [tex]s^2=3.45](https://tex.z-dn.net/?f=s%3Dsqrt%7B%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5E9%20%28x_i%20-%5Cbar%20x%29%5E2%7D%7Bn-1%7D%7D%0A%3C%2Fp%3E%3Cp%3EThe%20sample%20variance%20given%20was%20%5Btex%5Ds%5E2%3D3.45)
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: