Two shoemakers entered the competition, main goal of creating ten pairs of shoes, all sized

precisely at $26cm,$ equivalent of $401/2.$ Only precision of the size will be evaluated. The

following are the measurement of shoes' size:

Shoemaker A: $26\mathrm{.}06,26\mathrm{.}03,26\mathrm{.}09,26\mathrm{.}03,25\mathrm{.}99,26\mathrm{.}04,26\mathrm{.}01,26\mathrm{.}01,25\mathrm{.}99,25\mathrm{.}91$;

Shoemaker B: $25\mathrm{.}84,25\mathrm{.}89,26\mathrm{.}07,26\mathrm{.}09,26\mathrm{.}06,26\mathrm{.}03,26\mathrm{.}03,26\mathrm{.}06,26\mathrm{.}06,25\mathrm{.}85.$

In both cases, assume normality and have already tested at $5\%$ level of significance that

both shoemakers were successful and the mean values of size being equal to $26cm.$ Further,

to test the overall punctuality, i$.$e$.$ if the shoemakers are enough manually skilled to repeat

the correct size for every pair of shoes. Compare at $5\%$ significance level the deviation of

the size with a value of $0\mathrm{.}1$ in shoemaker $A$ by one$-$tailed test. Test if the variance in

shoemaker A is lower than in shoemaker B by a one$-$tailed test.