The distribution of class ranks in a particular introductory statistics class is assumed to be 20% freshmen, 40% sophomores, 35% juniors, and 5% seniors. To see if this is valid, a sample of 20 sections of this introductory statistics class is taken, and the frequency of each class rank is recorded. There are 130 freshmen, 242 sophomores, 221 juniors, and 37 seniors. The appropriate null hypothesis for a\(\style{font-family:Times New Roman;}{\chi^2}\)goodness-of-fit test would be:
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\(\style{font-family:Times New Roman;}{H_0:\;p_{fr}=0.20,\;p_{so}=0.40,\;p_{jr}=0.35,\;p_{sr}=0.05}\).
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\(\style{font-family:Times New Roman;}{H_0:\;p_{fr}=0.05,\;p_{so}=0.35,\;p_{jr}=0.40,\;p_{sr}=0.20}\).
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\(\style{font-family:Times New Roman;}{H_0:\;p_{fr}=130,\;p_{so}=242,\;p_{jr}=221,\;p_{sr}=37}\).
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\(\style{font-family:Times New Roman;}{H_0:\;p_{fr}=126,\;p_{so}=252,\;p_{jr}=220.5,\;p_{sr}=31.5}\).
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