Question

David Anderson has been working as a lecturer at Michigan State University for the last three years. He teaches two large sections of introductory accounting every semester. While he uses the same lecture notes in both sections, his students in the first section outperform those in the second section. He believes that students in the first section not only tend to get higher scores, they also tend to have lower variability in scores. David decides to carry out a formal test to validate his hunch regarding the difference in average scores. In a random sample of 18 students in the first section, he computes a mean and a standard deviation of 77.4 and 10.8, respectively. In the second section, a random sample of 14 students results in a mean of 74.1 and a standard deviation of 12.2.

Sample 1 consists of students in the first section and Sample 2 represents students in the second section. (You may find it useful to reference the appropriate table: z table or t table)


a. Construct the null and the alternative hypotheses to test David’s hunch.

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. In addition to assuming that the populations are normally distributed, what other assumption is used to conduct the test?

• Known population standard deviations.

• Unknown population standard deviations that are equal.

• Unknown population standard deviations that are not equal.

c. Implement the test at α = 0.01 using the critical value approach.

• Reject H₀; there is evidence that scores are higher in the first section.

• Reject H₀; there is no evidence that scores are higher in the first section.

• Do not reject H₀; there is evidence that scores are higher in the first section.

• Do not reject H₀; there is no evidence that scores are higher in the first section.

Answer 1

a)

H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b-1)

value of the test statistic t =0.798

b-2)

Unknown population standard deviations that are not equal.

c)

Do not reject H₀; there is no evidence that scores are higher in the first section.