A Statistics Professor at a Large University Hypothesizes That Students

question 105

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. Compute the appropriate test statistic to analyze the claim at the 1% significance level.

• A) t₇₀ = −2.811
• B) t₇₀ = 2.811
• C) z = −2.811
• D) z = 2.811

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Definitions:

Signal-Detection Theory

A means to quantify the ability to discern between information-bearing patterns and random patterns that distract from the information in the presence of uncertainty.

Just Noticeable Difference

The smallest change in intensity of a stimulus that can be detected by the sensory system.

Absolute Threshold

The minimum stimulus intensity required to be detectable by the senses.

Stimulus Intensity

The magnitude or strength of a stimulus, which can affect the perception and response of the sensory system to that stimulus.