A university is comparing the grade point averages of biology majors with the grade point averages of engineering majors. 25 students from each major are randomly selected. The mean and standard deviation for each sample are shown in the table.

Question

Sample Mean
- Biology Majors: 3.22
- Engineering Majors: 3.17

Sample Standard Deviation
- Biology Majors: 0.05
- Engineering Majors: 0.03

The university wants to test whether there is a significant difference in the GPAs for students in the two majors. What are the null and alternative hypotheses that should be used to test this claim?

A) null: μ_1 - μ_2 > 0; alternative: μ_1 - μ_2 < 0
B) null: μ_2 - μ_1 ≠ 0; alternative: μ_1 - μ_2 = 0
C) null: μ_1 - μ_2 = 0; alternative: μ_2 - μ_1 < 0
D) null: μ_1 - μ_2 = 0; alternative: μ_1 - μ_2 ≠ 0

Answer 1

To test whether there is a significant difference in the GPAs of biology majors and engineering majors, we need to set up the null and alternative hypotheses appropriately.

Let's denote:

• \( \mu_1 \) as the mean GPA of biology majors
• \( \mu_2 \) as the mean GPA of engineering majors

Since we are looking for a difference, the hypotheses can be set up as follows:

• Null Hypothesis (\(H_0\)): There is no difference in the means of GPAs between the two majors, which means \( \mu_1 - \mu_2 = 0 \).

• Alternative Hypothesis (\(H_a\)): There is a significant difference in the means of GPAs between the two majors, which can be expressed as \( \mu_1 - \mu_2 \neq 0 \) (indicating that the GPAs are different).

Given these descriptions, the correct option is:

D) null: \( \mu_1 - \mu_2 = 0 \); alternative: \( \mu_1 - \mu_2 \neq 0 \)