Question 135377: A vending machine company that dispenses coffee into cups must fill the cups with 7.8oz of liquid. Before selling the vending machine to a college or business, the company tests the machine to be sure it is dispensing an average amount of 7.8oz of coffee. A sample of 6 amounts is shown below. The amount of coffee is assumed to be normally distributed with a standard deviation of 0.10 oz. At the .10 level of significance, does the machine dispense as expected?
Treat as a small sample.
7.81 7.77 7.89 7.83 7.75 7.79
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A vending machine company that dispenses coffee into cups must fill the cups with 7.8oz of liquid. Before selling the vending machine to a college or business, the company tests the machine to be sure it is dispensing an average amount of 7.8oz of coffee. A sample of 6 amounts is shown below. The amount of coffee is assumed to be normally distributed with a standard deviation of 0.10 oz. At the .10 level of significance, does the machine dispense as expected?
Treat as a small sample.
7.81 7.77 7.89 7.83 7.75 7.79
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Ho: u = 7.8
Ha; u is not 7.8
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x-bar = 7.8067 ; s=0.04967
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Critical value for 2-tail t-test for alpha=10% and df=5: t =1.476
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Test statistic: t(7.8067) = (7.8067-7.8)/[0.04967/sqrt(6)] = 0.3304
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Conclusion: Since test stat is not in the reject interval, Fail to
reject Ho. The test provides statistical evidence that the machine
dispenses as expected.
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Cheers,
Stan H.
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