An educational researcher is interested in whether students do better in online classes as compared to on-ground classes. A random sample of 50 students was randomly assigned to participate in either an online or an on-ground statistics class. The final examination was the same for both classes, the grades of which are given in Table 11.15.

a. Using the Mann-Whitney test, determine if there is a difference in the population median examination scores between students who take online classes as compared to those who take on-ground classes.

b. Do you believe that the assumptions underlying the Mann-Whitney test have been violated?

c. Using an independent two-sample \(t\)-test, determine if there is a difference in the population mean examination scores between students who take online classes as compared to those who take on-ground classes.

d. Do you believe that the assumptions underlying the two-sample \(t\)-test have been violated?

e. Which analysis do you think is the most appropriate for the given data?

Table 11.15.

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Final Examination Scores for Students Randomly Assigned to an Online or On-ground Statistics Class Online 90 83 91 63 86 On-Ground 97 99 80 80 98 71 93 71 92 73 ERROR 74 62 91 90 73 60 71 83 93 65 73 86 71 87 97 93 77 91 97 92 74 85 77 82 97 ESSENFRESSES 74 97 79 97 77 99 91 84 92 71