Example $1.$ A random sample of $n=35$ observations from a quantitative population produced a mean $\stackrel{}{x}=2\mathrm{.}4$ and a standard deviation of $s=\mathrm{.}29.$ Your research objective is to show that the population mean $$ exceeds $2\mathrm{.}3.$ Use this information to answer the following questions below.

Note: This is a one$-$tailed test.

$15.$ Locate the rejection region for the test using a $5\%$ significance level.

$16.$ Do the data provide sufficient evidence to conclude that $>2\mathrm{.}3?$