SOLUTION: A report states that the average credit card debt for college seniors is $3262. The student senate at a particular college feels their seniors have a smaller debt. Their study of 5

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Question 422762: A report states that the average credit card debt for college seniors is $3262. The student senate at a particular college feels their seniors have a smaller debt. Their study of 50 randomly selected seniors found an average debt of $2995 with a standard deviation of $1100. Use a hypothesis test with a=.05 to determine if we can believe the students to be correct.
Answer by stanbon(75887) (Show Source):
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A report states that the average credit card debt for college seniors is $3262. The student senate at a particular college feels their seniors have a smaller debt. Their study of 50 randomly selected seniors found an average debt of $2995 with a standard deviation of $1100. Use a hypothesis test with a=.05 to determine if we can believe the students to be correct.
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Ho: u = 3262
Ha: u < 3262
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test stat: t(2995) = (2995-3262)/[1100/sqrt(50)] = -1.7163
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p-value = P(t< -1.7163 when df = 49) = 0.0462
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Since the p-value is < 5%, reject Ho.
The test supports the student's claim.
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Cheers,
Stan H.