A college student is interested in investigating the claim that students who graduate with a master's degree earn higher salaries, on average, than those who finish with a bachelor's degree. She surveys, at random, 33 recent graduates who completed their master's degrees and finds that their mean salary is [tex]$\$[/tex]32,200[tex]$ per year. The standard deviation of annual salaries for the population of recent graduates who have master's degrees is known to be $[/tex]\[tex]$2600$[/tex]. She also surveys, at random, 45 recent graduates who completed their bachelor's degrees and finds that their mean salary is [tex]$\$[/tex]31,400[tex]$ per year. The standard deviation of annual salaries for the population of recent graduates with only bachelor's degrees is known to be $[/tex]\[tex]$2100$[/tex]. Test the claim at the 0.01 level of significance. Let recent graduates with a master's degree be Population 1 and let recent graduates with a bachelor's degree be Population 2.
Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below.
[tex]$
\begin{array}{l}
H _0: \mu_1 = \mu_2 \\
H _a: \mu_1 \ \textgreater \ \mu_2
\end{array}
$[/tex]