Question

a college student is interested in investigating the claim that students who graduate with a masters degree earn higher salaries, on average, than those who finish with a bachelors degree. she surveys, at random, 34 recent graduates who completed their masters degrees, and finds that their mean salary is $39,800 per year. the standard deviation of annual salaries for the population of recent graduates who have masters degrees is known to be $900. she also surveys, at random, 31 recent graduates who completed their bachelors degrees, and finds that their mean salary is $39,000 per year. the standard deviation of annual salaries for the population of recent graduates with only bachelors degrees is known to be $1600. test the claim at the 0.05 level of significance. let recent graduates with a masters degree be population 1 and let recent graduates with a bachelors degree be population 2. step 1 of 3: state the null and alternative hypotheses for the test. fill in the blank below. $h_0:mu_1 = mu_2$ $h_a:mu_1$ ____ $mu_2$ answer: ≠ > <

Explanation:

Step1: Identify the claim

The claim is that students with master's degrees earn higher salaries on average than those with bachelor's degrees.

Step2: Define the hypotheses

The null hypothesis $H_0$ is a statement of no - effect or no difference. Here, $H_0:\mu_1=\mu_2$. The alternative hypothesis $H_a$ represents the claim we are trying to find evidence for. Since we want to test if master's degree holders have higher salaries, $\mu_1$ (mean salary of master's degree holders) should be greater than $\mu_2$ (mean salary of bachelor's degree holders).

Answer:

$H_a:\mu_1 > \mu_2$