A Statistics Professor at a Large University Hypothesizes That Students

question 9

Multiple Choice

A statistics professor at a large university hypothesizes that students who take statistics in the morning typically do better than those who take it in the afternoon. He takes a random sample of 36 students who took a morning class and, independently, another random sample of 36 students who took an afternoon class. He finds that the morning group scored an average of 74 with a standard deviation of 8, while the evening group scored an average of 68 with a standard deviation of 10. The population standard deviation of scores is unknown but is assumed to be equal for morning and evening classes. Let µ₁ and µ₂ represent the population mean final exam scores of statistics' courses offered in the morning and the afternoon, respectively. Which of the following hypotheses will test the professor's claim?

• A) H₀: µ₁ - µ₂ ≤ 0, H_A: µ₁ - µ₂ > 0
• B) H₀: µ₁ - µ₂ ≥ 0, H_A: µ₁ - µ₂ < 0
• C) H₀: µ₁ - µ₂ > 0, H_A: µ₁ - µ₂ ≤ 0
• D) H₀: µ₁ - µ₂ = 0, H_A: µ₁ - µ₂ ≠ 0

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Definitions:

Arithmetic Return

The simple average of a series of periodic returns of an investment.

Investment

The action of allocating resources, usually money, with the expectation of generating an income or profit.

Population

The total number of individuals within a specific area or of a particular species or group.

Rate of Return

The rate of return is the net gain or loss on an investment over a specified period, expressed as a percentage of the investment's initial cost.