Test the claim about the population mean, $,$ at the given level of significance using the given sample statistics.

Claim: $=30$;$=0\mathrm{.}02$;$=3\mathrm{.}77.$ Sample statistics: $\stackrel{}{x}=28\mathrm{.}1,n=74$

Identify the null and alternative hypotheses. Choose the correct answer below.

A$.H_0$:$<mn\; id="EditorElement\_62933">3</mn><mn\; id="EditorElement\_62934">0</mn>$

B$.H_0$:$=30$

$H_a$:$=30$

$H_a$:$>30$

C$.H_0$:$30$

D$.H_0$:$=30$

$H_a$:$=30$

$H_a$:$30$

E$.H_0$:$>30$

F$.H_0$:$=30$

$H_a$:$=30$

$H_a$:$<mn\; id="EditorElement\_62522">3</mn><mn\; id="EditorElement\_62523">0</mn>$

Calculate the standardized test statistic.

The standardized test statistic is

$($Round to two decimal places as needed.$)$

Determine the critical value$($s$).$ Select the correct choice below and fill in the answer box to complete your choice.