Q1 . Real data from a study reported in 1935 by B. Lowe of the lowa Agricultural Experiment Station . Donuts are traditionally a fried food and as such absorb some of the fat they are fried in . The amount and type of fat absorbed has implications for the healthfulness of the donuts . This study investigated whether there was any relationship between the quantitative variable " amount of fat absorbed " and a qualitative variable " type of fat " ( Fat 1 , Fat 2 , Fat 3 , Fat 4 ) . The data are as follows . Fat! Fat 2 Fat3 Fat 4 164 178 175\\ 155 2. 172 191 193 166 3 168 197 178 149 4 177 182 171 164 5 156 185 163\\ 170 6 195 177 176 168 ( a ) Conduct a test to determine whether or not the mean amount of fat absorbed is the same for all types of fats . Use level of significance a = 0. 05 . State your conclusion . Hint : ANOVA table is DE Sum Sq Mean Sq F value Pr ( > F ) 3 1636 545. 5 ? ? ? 0. 00688 * * X Residuals 20 2018 100 . 9 ( b ) Construct the 95 % confidence interval for the mean response level for Fat 1 . ( C ) Construct the 95% confidence interval for the difference between the factor level means 12 - 1.4