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A statistics professor at a large university hypothesizes that students who take statistics in the morning...

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Statistics

A statistics professor at a large university hypothesizes thatstudents who take statistics in the morning typically do betterthan those who take it in the afternoon. He takes a random sampleof 36 students who took a morning class and, independently, anotherrandom sample of 36 students who took an afternoon class. He findsthat the morning group scored an average of 72 with a standarddeviation of 8, while the evening group scored an average of 68with a standard deviation of 10. The population standard deviationof scores is unknown but is assumed to be equal for morning andevening classes. Let µ1 and µ2 represent the population mean finalexam scores of statistics' courses offered in the morning and theafternoon, respectively. Compute the appropriate test statistic toanalyze the claim at the 1% significance level.

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