A Statistics Professor at a Large University Hypothesizes That Students

question 55

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. At the 1% significance level, does the evidence support the professor's claim?

• A) No, because the test statistic is less than the critical value.
• B) Yes, because the test statistic is less than the critical value.
• C) No, because the test statistic is greater than the critical value.
• D) Yes, because the test statistic is greater than the critical value.