A national dairy manufactures products at facilities throughout the U$.$S$.$ To test the uniformity of its products four local sites were randomly chosen and samples of margarine produced at these sites were analyzed to determine the level of a particular fatty acid as a percentage of the fats. The data are recorded below. $($a$)$ Are there significant differences of variances among the manufacturing sites? $H_0$:${}_1^2={}_2^2={}_3^2={}_4^2=0\mathrm{.}05.(50)($b$)$ Are there significant differences of means in this characteristic among the manufacturing sites? $H_0$:${}_1={}_2={}_3={}_4=0\mathrm{.}05.(50)($c$)$ R codes to draw box plot using the data. $(10)($d$)$ R codes to test data normality, $(5)($e$)R$ codes to test homogeneity of variances among the manufacturing sites. $(10)($f$)$ R codes to test significant differences of means among the manufacturing sites. $(10)$

Site A B C D

$13\mathrm{.}5,13\mathrm{.}2,16\mathrm{.}8,18\mathrm{.}1$

$13\mathrm{.}4,12\mathrm{.}7,17\mathrm{.}2,17\mathrm{.}2$

$14\mathrm{.}1,12\mathrm{.}6,16\mathrm{.}4,18\mathrm{.}7$

$14\mathrm{.}2,13\mathrm{.}9,17\mathrm{.}3,18\mathrm{.}4$