Coca-Cola Bottling Co. Consolidated (CCBCC), headquartered in Charlotte, North Carolina, uses quality-control techniques to assure that the average amount of Coke in the cans is 12 ounces. It maintains that a small standard deviation of 0.05 ounces is acceptable. Any significant deviation in this standard deviation would negate any of the quality-control measures concerning the average amount of Coke in the 12-ounce cans. A sample of size 20 indicated that the standard deviation was 0.070.
a. Determine if the standard deviation of the amount of Coke in the cans differs from the standard deviation specified by the quality control division. Use a significance level of 0.10.
b. The quality-control sampling occurs several times a day. In one day, seven samples were taken, and three indicated that the standard deviation was not 0.05. If the seven samples were taken at a time in which the standard deviation met specifications, determine the probability of having at least three out of seven samples indicate the specification was not being met.