Question

A study of recent UniSIM graduates reveals that for a sample of 10 "Accounting" majors, the mean salary was $30,000 per year. The sample standard deviation is $2000. A sample of 8 "General Business" majors reveals a mean salary of $29,000 per year with a standard deviation of $1500. A two-sample t-test is carried out to determine whether we can conclude that "Accounting" majors earn more than "General Business" majors at the significance level α = 0.05. Suppose µ1 refers to "Accounting" majors (graduates) and µ2 refers to "General Business" majors (graduates). Formulate the null and alternative hypothesis.

a) H0: µ1 ≤ µ2, H1: µ1 > µ2
b) H0: µ1 = µ2, H1: µ1 ≠ µ2
c) H0: µ1 ≥ µ2, H1: µ1 < µ2
d) None of the above.

Answer 1

The correct null and alternative hypotheses to test whether 'Accounting' majors earn more than 'General Business' majors are H0: μ1 ≤ μ2 and H1: μ1 > μ2, respectively.

Step-by-step explanation:

The null and alternative hypothesis for the scenario where we want to determine whether 'Accounting' majors earn more than 'General Business' majors are as follows:

• Null Hypothesis – H0: μ1 ≤ μ2, which states that the mean salary of 'Accounting' majors is less than or equal to that of 'General Business' majors.
• Alternative Hypothesis – H1: μ1 > μ2, which states that the mean salary of 'Accounting' majors is greater than that of 'General Business' majors.

This is because the research question is specifically asking if 'Accounting' majors earn more, which indicates a one-sided hypothesis test is appropriate. In this case, the correct formulation of the hypotheses would be option (a).