Returning to the compilation times, in milliseconds, for each of five programs, run on four compilers.

Test, at the $1\%$ significance level, the hypothesis that there is no difference between the performance of the four compilers.

Has the use of programs as a blocking factor proved worthwhile? Explain.

The data, given earlier, are reproduced below.

$\backslash$table$[[,4,$Compiler,,$],[$Program A$,29\mathrm{.}21,28\mathrm{.}25,28\mathrm{.}20,28\mathrm{.}62],[$Program B$,26\mathrm{.}18,26\mathrm{.}02,26\mathrm{.}22,25\mathrm{.}56],[$Program C$,30\mathrm{.}91,30\mathrm{.}18,30\mathrm{.}52,30\mathrm{.}09],[$Program D$,25\mathrm{.}14,25\mathrm{.}26,25\mathrm{.}20,25\mathrm{.}02],[$Program E$,26\mathrm{.}16,25\mathrm{.}14,25\mathrm{.}26,25\mathrm{.}46]]$