The following statistics are calculated by sampling from four normal populations whose variances are equal: $($You may find it useful to reference the t table and the q table.$)$

x$1$

$=137,$ n$1=5$; x$2$

$=149,$ n$2=5$; x$3$

$=143,$ n$3=5$; x$4$

$=136,$ n$4=5$; MSE $=45\mathrm{.}6$

a$.$ Use Fisher$$s LSD method to determine which population means differ at $\backslash$alpha $=0\mathrm{.}05.($Negative values should be indicated by a minus sign. Round final answers to $2$ decimal points.$)$

b$.$ Use Tukey$$s HSD method to determine which population means differ at $\backslash$alpha $=0\mathrm{.}05.($If the exact value for nT $$ c is not found in the table, then round down. Negative values should be indicated by a minus sign. Round your answers to $2$ decimal places.$)$