Question: Cellulose content in alfalfa hay. An agronomist examines the cellulose content of a variety of alfalfa hay. Suppose that the cellulose content in the population has standard deviation \(\sigma=8\) milligrams per gram \((\mathrm{mg} / \mathrm{g}) . \mathrm{A}\) sample of 15 cuttings has mean cellulose content \(\pi=145 \mathrm{mg} / \mathrm{g}\)

1. Give a \(90 \%\) confidence interval for the mean cellulose content in the population.
2. A previous study claimed that the mean cellulose content was \(\mu=140 \mathrm{mg} / \mathrm{g}\), but the agronomist believes that the mean is higher than that figure. State \(H_{0}\) and \(H_{a}\) and carry out a significance test to see if the new data support this belief.
3. The statistical procedures used in parts (a) and (b) are valid when several assumptions are met. What are these assumptions?

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