An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on $190$

engines and the mean pressure was $7\mathrm{.}1$

lbs$/$square inch. Assume the variance is known to be $0\mathrm{.}81$

$.$ If the valve was designed to produce a mean pressure of $7\mathrm{.}2$

lbs$/$square inch, is there sufficient evidence at the $0\mathrm{.}05$

level that the valve does not perform to the specifications?

State the null and alternative hypotheses for the above scenario.