The industrial world shares this common goal: Improve quality by reducing variation. Quality control engineers want to ensure that a product has an acceptable mean, but they also want to produce items of consistent quality so that there will be few defects. The Newport Bottling Company had been manufacturing cans of cola with amounts having a standard deviation of 0.051 oz. A new bottling machine is tested, and a simple random sample of 24 cans results in the amounts (in ounces) listed below.

11.98 11.98 11.99 11.98 11.90 12.02 11.99 11.93

12.02 12.02 12.02 11.98 12.01 12.00 11.99 11.95

11.95 11.96 11.96 12.02 11.99 12.07 11.93 12.05

(a) Use a 0.05 signicance level to test the claim that cans of cola from the new machine have amounts with a standard deviation that is

less than 0.051 oz.

(b) Which method is used above and why. Is there any other method that could have also been used if yes, why. If not, why not.

(c) In general, how do you nd a rejection region for two tailed tests, left tailed test and right tailed test in such tests. Explain.

(d) Is it a parametric or non parametric test, explain. If it is parametric then what is the distribution of the test statistic and why explain.