Question: One of the accusations made about tobacco companies is that they add nicotine to their cigarettes, which makes them even more addictive to smokers. Tobacco company scientists argue that the amount of nicotine in cigarettes depends completely on the size of the tobacco leaf. That is, during poor growing seasons the tobacco leaves are smaller than in normal growing seasons. Since it is widely believed that the amount of nicotine in a leaf is a fixed quantity, smaller leaves would result in cigarettes having more nicotine (since a greater fraction of the leaf would be used to make a cigarette). A university chemist took simple random samples of tobacco leaves where the amount of water available to the plants was varied. Three different groups of tobacco leaves were grown. Group 1 were grown with about an average season’s rainfall; group 2 leaves were given about 67% of group 1’s water; and group 3 leaves were given 33% of group 1’s water. The size of each fully grown leaf was measured and is stored in the data file NICOTINE.

(a) At the 1% level of significance, test whether there is a difference in the size of tobacco leaves between the three growing seasons (average season rainfall, 67% of average season rainfall, 33% of average season rainfall). (6 marks)

(b) Is there evidence to support the company’s claim that the poorer the growing season the smaller the tobacco leaves? Explain. (4 marks)