A car manufacturer, Swanson, claims that the mean lifetime of one of its car engines is greater than $220,001$ miles, which is the mean lifetime of the engine of a competitor. The mean lifetime for a random sample of $23$ of the Swanson engines was x $=226,450$ miles with a standard deviation, s$,$ of $11,502$ miles. Test the Swanson's claim using a significance level of $=0\mathrm{.}02.$

A$.$

P$-$value $=0\mathrm{.}00670<0\mathrm{.}02,$ reject the null hypothesis. There is enough evidence to conclude that the mean lifetime of this car engine is greater than $220,001$ miles.

B$.$

P$-$value $=0\mathrm{.}00431<0\mathrm{.}01,$ reject the null hypothesis. There is enough evidence to conclude that the mean lifetime of this car engine is greater than $220,001$ miles.

C$.$

P$-$value $=0\mathrm{.}01341<0\mathrm{.}05,$ reject the null hypothesis. There is enough evidence to conclude that the mean lifetime of this car engine is greater than $220,001$ miles.

D$.$

P$-$value $=0\mathrm{.}02670<0\mathrm{.}05,$ reject the null hypothesis. There is enough evidence to conclude that the mean lifetime of this car engine is greater than $220,001$ miles.