A drilling machine is used to make rivet holes in aluminium plates used in

aircraft manufacture. If the standard deviation of the hole diameter exceeds

$0\mathrm{.}01$ millimetres there is an unacceptably high probability that the rivet will not

fit. A random sample of $15$ rivet holes showed a sample average of $0\mathrm{.}215$

millimetres and a sample standard deviation of $0\mathrm{.}008$ millimetres. Perform an

appropriate hypothesis test to determine if there strong evidence $($as the

engineer claims$)$ to indicate the standard deviation of the hole diameter

exceeds $0\mathrm{.}01$ millimetres. $0\mathrm{.}05$ significane