SOLUTION: Bottles of a popular cola are supposed to contain 300ml of cola. There is some variation from to bottle to bottle because the filling machinery is not perfectly precise. The distri

Question 542551: Bottles of a popular cola are supposed to contain 300ml of cola. There is some variation from to bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of Q=3 ml. An inspector who suspects that the bottler is underfilling measures the contents of six bottles. The results are
299.4 297.7 301.0
298.9 300.2 297.0
Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300 ml? perform a significance test at the Q= .05level.
Z=(300-299.03)/3/6= .79 Please help

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Bottles of a popular cola are supposed to contain 300ml of cola. There is some variation from to bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of Q=3 ml. An inspector who suspects that the bottler is underfilling measures the contents of six bottles. The results are
299.4 297.7 301.0
298.9 300.2 297.0
----
sample mean = x-bar = 299.03
Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300 ml? perform a significance test at the Q= .05level.
Ho: u >= 300
Ha: u < 300 (claim)
---
test statistic: t(299.03) = (299.03-300)/[1.5/sqrt(6)] = -1.5840
----
p-value = P(t < -1.5840 when df = 5) = 0.0870
----
Conclusion:
Since the p-value is greater than 5% fail to reject Ho.
The test results do not support the claim.

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Cheers,
Stan H.
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