Question 557083: 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 hyposthesis that the true mean is 520?
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?::: the t-distribution
Why?::: small sample
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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 ml (claim)
Ha: u # 520 ml
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Reject Ho is t < -2.26 or if t > 2.26
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C) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hyposthesis that the true mean is 520?
t(515) = (515-520)/[4/sqrt(16)] = -5/1 = -5
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Since t = -5 is in the reject interval, reject Ho.
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Cheers,
Stan H.
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