Question 320873: Prior to the expansion of the civic library, it was determined that 400 books were loaned out per day, on average. It was believed that the expansion would increase the mean number of books loaned out per day.
After completion of the expansion, a random sample of 60 days showed that, on average, 425 books were loeaned out per day with a standard deviation of 70 books per day.
Does the sample result indicate that the mean number of books loaned out per day increased? Formulate and test the appropriate hypotheses at the 5% level of significance. Use the critical value approach
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Prior to the expansion of the civic library, it was determined that 400 books were loaned out per day, on average. It was believed that the expansion would increase the mean number of books loaned out per day.
After completion of the expansion, a random sample of 60 days showed that, on average, 425 books were loaned out per day with a standard deviation of 70 books per day.
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Ho: u = 400
Ha: u > 400
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Does the sample result indicate that the mean number of books loaned out per day increased? Formulate and test the appropriate hypotheses at the 5% level of significance. Use the critical value approach
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Critical value for right tail test with alpha = 5% and df=59
= invT(0.95,59) = 1.6711
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test statistic: t(425) = (425-400)/[70/sqrt(60)] = 2.7664
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Conclusion: Since the ts is in the reject interval, reject Ho.
The test does not support the conclusion that the mean is 400.
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Cheers,
Stan H.
test stat:
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