A company purchases large quantities of solvent in 50-gallon barrels. The purchasing agent has become concerned that the supplier has been under filling the barrels. A random sample of n=10 barrels contained the following amounts of solvent (in gallons):
49.3, 48.7, 50.1, 50.2, 47.9, 48.3, 49.8, 50.0, 49.5, 49.1
a) Compute the mean and standard deviation for the above sample.
b) Develop a 95% confidence interval for µ, the true mean amount of solvent in a barrel. Interpret your results.
c) Develop a 95% prediction interval for the amount of solvent in a barrel. Interpret your results.
d) Given the above results are the barrels being under filled? Explain.
e) What did you assume to do the analyses? Can you evaluate how well these data meet the assumptions?