Question 130980: At Ajax Spring Water, a 1/2 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 twotailed decision rult 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 that contradict the hypothesis that the true mean is 520ml?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! At Ajax Spring Water, a 1/2 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?
The t-distribution which is suitable for small-sample testing.
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(B) Set up hypotheses and a twotailed decision rule for the correct mean using the 5 percent level of significance.
Ho: mu = 520
Ha: mu is not equal to 520
Critical values for alpha = 5% and 9 degrees of freedom : t = +-1.833
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(C) If a sample of 16 bottles shows a mean fill of 515 ml, does that contradict the hypothesis that the true mean is 520ml?
Critical values for alpha=5% and 15 degrees of freedom : t= +-1.753
Test statistic: t(515)=(515-520)/[4/sqrt(16)]=-5*4/4 = -5
Conclusion: Since -5 < -1.753, reject Ho; this contradicts the hypothesis
that the true mean is 520 ml.
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Cheers,
Stan H.
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