A study of fill volumes is conducted at a food canning factory to determine the level of consistency between the two filling lines, A and B. A random sample of 11 cans taken from line A has a sample average of 8.005 ounces and a sample standard deviation of 0.013 ounces. A similar sample of 16 cans is obtained from line B with a sample average of 7.997 ounces and a sample standard deviation of 0.008 ounces. The quality control manager is interested in finding evidence that there is a difference in the variance in fill volume for the two lines.
1. Give the value of the test statistic suggested by the testing situation described above.
2. p-value
3. What critical value(s) would be used at the .05 significance level?
4. What is the decision at the .05 significance level?
5. Considering the test conducted in #1-4, if you were to construct a 95% confidence interval for the ratio of the two variances, which of the following would you expect to be true concerning the two values describing the interval?
a. one negative, one positive
b. both less than one
c. one less than 1, one greater than 1
d. both greater than 1
e. both negative