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:

Amos Tversky

A cognitive and mathematical psychologist known for his collaborative work with Daniel Kahneman on the cognitive biases affecting human judgment and decision-making.

Morale Problem

A situation in which there is widespread dissatisfaction, lack of enthusiasm, or disengagement among members of a group or organization.

Bounded Rationality

A concept suggesting that decision-makers are limited by the information they have, the cognitive limitations of their minds, and the finite amount of time they have to make decisions.

Maximization

The process of seeking the highest possible outcome or result from a set of choices or actions.