14. The cigarette experiment was conducted in order to determine the factors that affect the length of time that a cigarette will burn. There were three factors of interest: \"Tar\" (factor A) at two levels, \"regular\" and \"ultra-light,\" \"Brand\" (factor B) at two levels, \"name brand\" and \"generic brand\" (coded 1 and 2), \"Age\" (factor C) at three levels, \"fresh,\" \"24 hour air exposure,\" \"48 hour air exposure.\" The cigarettes were to be burned in whole plots of size six. This was to help with the difficulty of recording burning times and to help keep the amount of smoke in the room at a reasonable level. There were ten whole plots, and these were assigned at random to the tar levels so that each tar level was assigned five whole plots. The six split plots (time slots) in each whole plot were assigned at random to the six brand/age treatment combinations. Marks were made across the seam of each cigarette at a given distance apart. Each cigarette was lit at the beginning of its allotted time slot, and the time taken to burn between the two marks was recorded. The data are shown below: Whole Plot (Time) A (Tar) 1 1 22 (301) 11 (326) 23 (260) 13 (290) 12 (312) 21 (292) 2 2 11 (329) 12 (331) 13 (285) 21 (306) 22 (258) 23 (276) 3 2 22 (290) 11 (380) 12 (335) 13 (309) 23 (243) 21 (334) 4 2 11 (321) 21 (337) 23 (275) 12 (316) 13 (307) 22 (250) 5 2 22 (308) 11 (345) 21 (307) 23 (288) 13 (321) 12 (330) 6 1 11 (344) 23 (283) 21 (281) 22 (261) 13 (307) 12 (292) 7 1 21 (274) 13 (310) 12 (304) 22 (279) 23 (277) 11 (330) 8 1 13 (302) 12 (325) 22 (301) 11 (338) 23 (270) 21 (297) 9 2 12 (323) 13 (334) 23 (265) 11 (326) 22 (269) 21 (297) 10 1 23 (309) 13 (314) 22 (259) 11 (344) 21 (310) 12 (322) Levels of BC (Burning times in seconds) (i) Write the linear model for this experiment and explain the terms. (ii) Construct an analysis of variance table and test the hypotheses that you think are of interest. State your conclusions. (iii) Use Tukey's method to examine the pairwise differences in the effects on burning time of the six BC treatment combinations (averaged over tar levels). (iv) Examine the linear and quadratic trends of burning time due to different ages, for each brand separately. (v) State your conclusions about the experiment, including your choice of overall significance levels and overall confidence levels