Question: Coffee containers are packaged by weight, and are supposed to hold 454 grams of coffee. There is some natural variation in the filling process, so not all containers will hold exactly 454 grams. The quality control manager is comfortable with the variation provided the standard deviation of coffee per container does not exceed 10 grams. A recent random sample of 20 containers showed a mean weight of 453.5 grams, and a standard deviation of 5 grams.

a) Use the results of the sample to construct a 98% confidence interval for the population standard deviation of weights.

b) Does the confidence interval suggest that the standard deviation of weights is a an acceptable level?