Answer :
To correctly state the null and alternative hypotheses for this test, we need to clearly establish our assumptions about the population means for the two groups under consideration.
In this case:
- Population 1 consists of recent graduates with a master's degree.
- Population 2 consists of recent graduates with a bachelor's degree.
Null Hypothesis ([tex]\( H_0 \)[/tex]): The null hypothesis always states that there is no effect or no difference. Here, it means that the average salary of graduates with a master's degree is equal to the average salary of graduates with a bachelor's degree.
[tex]\[ H_0: \mu_1 = \mu_2 \][/tex]
Alternative Hypothesis ([tex]\( H_1 \)[/tex]): The alternative hypothesis states that there is a difference. In this context, the student is interested in investigating whether graduates with a master's degree earn higher salaries than those with a bachelor's degree. This implies a one-sided test where we are checking if the mean salary of master's degree graduates is greater than that of bachelor's degree graduates.
[tex]\[ H_1: \mu_1 > \mu_2 \][/tex]
Hence, the correct null and alternative hypotheses are:
[tex]\[ \begin{array}{l} H _0: \mu_1 = \mu_2 \\ H _1: \mu_1 > \mu_2 \end{array} \][/tex]
So the initial step for the hypothesis test is clearly defined.
In this case:
- Population 1 consists of recent graduates with a master's degree.
- Population 2 consists of recent graduates with a bachelor's degree.
Null Hypothesis ([tex]\( H_0 \)[/tex]): The null hypothesis always states that there is no effect or no difference. Here, it means that the average salary of graduates with a master's degree is equal to the average salary of graduates with a bachelor's degree.
[tex]\[ H_0: \mu_1 = \mu_2 \][/tex]
Alternative Hypothesis ([tex]\( H_1 \)[/tex]): The alternative hypothesis states that there is a difference. In this context, the student is interested in investigating whether graduates with a master's degree earn higher salaries than those with a bachelor's degree. This implies a one-sided test where we are checking if the mean salary of master's degree graduates is greater than that of bachelor's degree graduates.
[tex]\[ H_1: \mu_1 > \mu_2 \][/tex]
Hence, the correct null and alternative hypotheses are:
[tex]\[ \begin{array}{l} H _0: \mu_1 = \mu_2 \\ H _1: \mu_1 > \mu_2 \end{array} \][/tex]
So the initial step for the hypothesis test is clearly defined.