Question 179243: When a 1/2 liter bottle of a liquid drink is supposed to contain a mean of 520 ml and it has a known process standard deviation of 4 ml, which sampling distribution would be used if random samples of 10 bottles are to be weighed? and Why? How do I set up a hypothesis and a two-tailed decision rule for the correct mean using the 5% level of signifance? Also when the sample of 16 bottles shows a mean fill of 515 ml does this contradict the hypothesis that the true mean is 520 ml? #952
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! When a 1/2 liter bottle of a liquid drink is supposed to contain a mean of 520 ml and it has a known process standard deviation of 4 ml, which sampling distribution would be used if random samples of 10 bottles are to be weighed? and Why?
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Ans: The t-distribution because you are testing a small sample for the validity
of a population mean.
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How do I set up a hypothesis and a two-tailed decision rule for the correct mean using the 5% level of signifance?
Ho: u = 520
Ha: u is not equal to 520
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Critical value for 2-tail t-test with alpha=5% and df=9 is +-2.262
Rule: If the test statistic if less than -2.262 of greater than 2.262,
reject Ho.
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Also when the sample of 16 bottles shows a mean fill of 515 ml does this contradict the hypothesis that the true mean is 520 ml?
test statistic: t(515) = (515-520)/[4/sqrt(16)] = -5
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Conclusion: Since -5 is less than -2.262, reject Ho.
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Cheers,
Stan H.
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