A Statistics Professor at a Large University Hypothesizes That Students

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 independently random samples,each of size 36,consisting of students who took a morning and an afternoon class,and compares the scores of each group on a common final exam.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 andµ₂ 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