Question 170645This question is from textbook
: 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?
This question is from textbook
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?
Mean of the sample means: 520 ml
St. Dev. of the sample means: 4/sqrt(10)
Both are prescribed by the Central Limit Theorem
-----------------------------------------------------------
(b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance.
Ho: mean = 520
Ha: mean is not 520
Reject Ho if z(mean of the sample) is > 1.96 or <-1.96
------------------------------------------------------------
(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?
z(515) = (515-520)/[4/sqrt(10)]= -3.9528...
Yes, it is evidence the mean is not 520.
============================================
Cheers,
Stan H.
|
|
|
