Prairie Flower Cereal, Inc., has asked you to study the variability of the weights of cereal bags produced in plant 2, located in rural Malaysia. The package weights are known to be normally distributed. Using a random sample of n = 71, you find that the sample mean weight is 40 and the sample variance is 50.
The marketing vice president claims that there is a very small probability that the population mean weight is less than 39. Use an appropriate statistical analysis and comment on his claim.