Excess cellulose in alfalfa reduces the â€œrelative feed valueâ€ of the product that will be fed to dairy cows. If the cellulose content is too high, the price will be lower and the producer will have less profit. An agronomist examines the cellulose content of one type of alfalfa hay. Suppose that the cellulose content in the population has standard deviation Ïƒ = 8 milligrams per gram (mg/g). A sample of 15 cuttings has mean cellulose content x = 145 mg/g.
(a) Give a 90% confidence interval for the mean cellulose content in the population.
(b) A previous study claimed that the mean cellulose content was Î¼ = 140 mg/g, but the agronomist believes that the mean is
higher than that figure. State H0 and Ha and carry out a significance test to see if the new data support this belief.
(c) The statistical procedures used in (a) and (b) are valid when several assumptions are met. What are these assumptions?