Q$\mathrm{.}7\mathrm{.}5$ In a particular state an examination was administered to a number of schools with mean score of $62\mathrm{.}5$ and the standard deviation of $6\mathrm{.}7.$ For a given school where $180$ students took the same examination the mean score was $63\mathrm{.}8.$ Perform a test of significance at $5\%$ level by:

$($a$)$ A one$-$tailed test, and

$($b$)$ A two$-$tailed test, and discuss the results.