A machine is set to produce a product whose diameter is 40 cm. The company is concerned about the variation in the diameter of the product because if there is significant variation in the standard deviation of the diameter then the product must be thrown away. A random sample of 21 items was selected and sample standard deviation of the diameter was computed. The sample results are shown below:
Sample Size = 21
Sample Standard Deviation = S = 0.005
Using the sample data provided, you want to construct a 90% confidence interval estimate for the true population variance, σ2 for the product's diameter. In order to do so you must first determine the appropriate values from the χ2 distribution for computing the confidence interval.
The upper and lower tail critical values of the χ2 distribution that are used to construct the 90% confidence interval for this problem would be:
a. = 10.8508 = 31.4104
b. = 11.5913 = 32.6706
c. = 12.4426 = 28.4120
d. = 31.4104 = 39.9969