Three different methods were used to determine the dissolved$-$oxygen content of the lake water. Each of the three methods was applied to a sample of water six times, with the following results. Are there significant differences of variances in DO content among lakes? $H_0$:${}_1^2={}_2^2={}_3^2={}_4^2*=0\mathrm{.}05.(50)($b$)$ Are there significant differences of means in DO content among lakes? $H_0$:${}_1={}_2={}_3={}_4,=0\mathrm{.}05.(50)($c$)$ R codes to draw box plot using the data. $(5)($d$)R$ codes to test data normality, $(5)($e$)R$ codes to test homogeneity of variances among the manufacturing sites. $(5)($f$)R$ codes to test significant differences of means among the manufacturing sites. $(5)$

$\backslash$table$[[$Method $1,$Method $2,$Method $3],[10\mathrm{.}36,10\mathrm{.}88,10\mathrm{.}73],[10\mathrm{.}77,10\mathrm{.}75,10\mathrm{.}79],[10\mathrm{.}30,10\mathrm{.}80,10\mathrm{.}78],[10\mathrm{.}69,10\mathrm{.}81,10\mathrm{.}82],[10\mathrm{.}87,10\mathrm{.}70,10\mathrm{.}88],[10\mathrm{.}60,10\mathrm{.}82,10\mathrm{.}81]]$

TABLE B$.4($cont$.)$: Critical Values of the F Distribution

$()1$ Numerator $DF=2$

$\backslash$table$[[n_2=,(2)$:$0\mathrm{.}50,0\mathrm{.}20,0\mathrm{.}10,0\mathrm{.}05,0\mathrm{.}02,0\mathrm{.}01,0\mathrm{.}005],[$Denom$.$ DF$,(1)$:$0\mathrm{.}25,0\mathrm{.}10,0\mathrm{.}05,0\mathrm{.}025,0\mathrm{.}01,0\mathrm{.}005,0\mathrm{.}0025],[1,7\mathrm{.}50,49\mathrm{.}5,200.,800.,5000.,20000.,80000.],[2,3\mathrm{.}00,9\mathrm{.}00,19\mathrm{.}0,39\mathrm{.}0,99\mathrm{.}0,199.,399.],[3,2\mathrm{.}28,5\mathrm{.}46,9\mathrm{.}55,16\mathrm{.}0,30\mathrm{.}8,49\mathrm{.}8,79\mathrm{.}9],[4,2\mathrm{.}00,4\mathrm{.}32,6\mathrm{.}94,10\mathrm{.}6,18\mathrm{.}0,26\mathrm{.}3,38\mathrm{.}0],[5,1\mathrm{.}85,3\mathrm{.}78,5\mathrm{.}79,8\mathrm{.}43,13\mathrm{.}3,18\mathrm{.}3,25\mathrm{.}0],[6,1\mathrm{.}76,3\mathrm{.}46,5\mathrm{.}14,7\mathrm{.}26,10\mathrm{.}9,14\mathrm{.}5,19\mathrm{.}1],[7,1\mathrm{.}70,3\mathrm{.}26,4\mathrm{.}74,6\mathrm{.}54,9\mathrm{.}55,12\mathrm{.}4,15\mathrm{.}9],[8,1\mathrm{.}66,3\mathrm{.}11,4\mathrm{.}46,6\mathrm{.}06,8\mathrm{.}65,11\mathrm{.}0,13\mathrm{.}9],[9,1\mathrm{.}62,3\mathrm{.}01,4\mathrm{.}26,5\mathrm{.}71,8\mathrm{.}02,10\mathrm{.}1,12\mathrm{.}5],[10,1\mathrm{.}60,2\mathrm{.}92,4\mathrm{.}10,5\mathrm{.}46,7\mathrm{.}56,9\mathrm{.}43,11\mathrm{.}6]]$

$\backslash$table$[[$v$,,0\mathrm{.}999,,,,$TABL,rit,ue:$,$Chi$-,,$ribut,,,$],[1,,,0\mathrm{.}90,0\mathrm{.}975,0\mathrm{.}95,0\mathrm{.}90,0\mathrm{.}75,0\mathrm{.}50,0\mathrm{.}25,0\mathrm{.}10,0\mathrm{.}05,0\mathrm{.}025,0\mathrm{.}01],[\frac{2}{3},0\mathrm{.}002,\backslash$table$[[0\mathrm{.}000],[0\mathrm{.}000]],0\mathrm{.}000,0\mathrm{.}001,0\mathrm{.}004,0\mathrm{.}016,,,,2706,3\mathrm{.}841,5\mathrm{.}024,6\mathrm{.}635],[3,0024,\backslash$table$[[0\mathrm{.}010],[0\mathrm{.}07]],0\mathrm{.}020,0\mathrm{.}051,0\mathrm{.}103,0211,,0\mathrm{.}455,\backslash$table$[[1\mathrm{.}323],[2\mathrm{.}773]],,5\mathrm{.}991,7\mathrm{.}378,9\mathrm{.}210],[4,0\mathrm{.}991,0\mathrm{.}072,0\mathrm{.}115,0\mathrm{.}216,0\mathrm{.}352,,0\mathrm{.}575,1\mathrm{.}386,2\mathrm{.}773,\backslash$table$[[4\mathrm{.}605],[6\mathrm{.}251]],7\mathrm{.}815,9\mathrm{.}348,11\mathrm{.}345],[1,0\mathrm{.}210,\backslash$table$[[0\mathrm{.}207],[0\mathrm{.}412]],0\mathrm{.}297,0\mathrm{.}484,0\mathrm{.}711,\backslash$table$[[0\mathrm{.}584],[1\mathrm{.}064]],1\mathrm{.}213,2\mathrm{.}366,\backslash$table$[[4\mathrm{.}108],[5\mathrm{.}385]],7\mathrm{.}779,9\mathrm{.}488,11\mathrm{.}143,13\mathrm{.}277],[,,,0\mathrm{.}554,0\mathrm{.}831,1\mathrm{.}145,1\mathrm{.}610,\backslash$table$[[1\mathrm{.}923],[2\mathrm{.}675]],3\mathrm{.}357,\backslash$table$[[5\mathrm{.}385],[6\mathrm{.}626]],9\mathrm{.}236,11\mathrm{.}070,12\mathrm{.}833,150\%6$