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.

Question

Quizplus · Accepted Answer

Given the information, we are dealing with a hypothesis test comparing two means with unknown but assumed equal population standard deviations. The professor's claim suggests a directional hypothesis where the mean score of the morning class (µ1) is greater than the mean score of the afternoon class (µ2). The calculation of the test statistic would involve the difference in sample means, the standard deviations, and the sample sizes. The fact that the morning class has a higher average score with a significant difference supports the claim, assuming the calculation of the test statistic and its comparison to the critical value at the 1% significance level shows it exceeds the critical value. This would lead to rejecting the null hypothesis (that there is no difference or the morning class does not score higher) in favor of the alternative hypothesis (the morning class scores higher), thus supporting the professor's claim.

A Statistics Professor at a Large University Hypothesizes That Students