SOLUTION: At Ajax Spring Watewr, a half-liter bottle of soft dring is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard de

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Question 285680: At Ajax Spring Watewr, a half-liter bottle of soft dring is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. (a) which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why? (b) Set up hypothesis and a two-tailed decision rule for the correct mean using the 5 percent level of significance. (c) I f a sample of 16 bottles shows a mean fill of 515 ml. does this contradict the hypothesis that the true mean is 520 ml?
Answer by stanbon(75887) About Me  (Show Source):
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At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml.
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(a) which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?
Note: Text books differ on whether a z or a t distribution should be used.
Large numbers of the better stat teachers say we should use the t distribution
on ALL tests of the population mean. Others say use t only if the sample
size is less that 30.
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(b) Set up hypothesis and a two-tailed decision rule for the correct mean using the 5 percent level of significance.
Ho: u = 520
Ha: u is not equal to 520
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Reject Ho if the test statistic is less than invT(0.025 with df = 9)=-2.2622
or the test stat is greater than 2.2622)
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(c) If a sample of 16 bottles shows a mean fill of 515 ml. does this contradict the hypothesis that the true mean is 520 ml?
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t(515) = (515-520)/[4/sqrt(16)] = -5
The critical values are +-invT(0.025 with df=15) = +-2.1314..
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Conclusion: Since the test stat is in the reject interval,
reject Ho that the mean is 520.
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Cheers,
Stan H.
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