8.2 A professor suspects that the heaviest library users are sophomores and juniors, perhaps because freshmen haven’t yet learned to take advantage of all library resources, and perhaps because seniors have their minds more on postgraduate activities than on getting good grades in their last year. At any rate, he knows that the student body is 50% freshmen, 25% sophomores, 10% juniors, and 15% seniors. A random sample of 1,000 library users turns out to be composed of 480 freshmen, 290 sophomores, 180 juniors, and 50 seniors. Use the chi-square goodness-of-fit test to decide whether or not these frequencies support the professor’s guess. Use the 5% level of significance,
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