Question 198410: 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.
(a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?
(b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent
level of significance.
(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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
(a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?
The "t" distribution because the samples are small.
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(b) Set up hypotheses 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
Reject Ho is the test statistic is less than -2.262 or greater than +2.262
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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?
Note: You have changed the sample size.
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t(515) = (515-520)/[4/Sqrt(16)] = -5
The p-value for a 2-tail test with t = -5 and df=15 = 2[P(t<-5)]=0.000158
Since the p-value is less than 5%, reject Ho.
The test does not support the claim that the mean amount is 520 mL.
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Cheers,
Stan H.
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