Solve the Problem on the Issue of Mustard Seed in Your Economy Size Packages

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1. 
Assume you are the manager of a mustard seed factory in Colombia.
Your company has received complaints that there isn’t enough mustard seed in
your economy size packages, which should have 1.7 ounces.  You ask your foreman and chief operating
officer Juan Valdez to test the new mustard seed packaging machine you are
installing. He runs a sample of 36 packages, with the results of package sizes
in ounces:

Data Set

1.5

1.7

1.8

1.9

1.7

1.75

1.75

1.66

1.81

1.65

1.77

1.75

1.8

2.2

1.7

1.65

1.88

1.6

1.7

1.7

1.6

1.65

1.65

1.65

1.8

1.91

1.7

1.59

1.76

1.65

1.3

2.0

1.91

1.65

1.8

1.8

  1. Calculate a 95% confidence interval on the
    average weight of packaged mustard seed. Explain very carefully to the
    packaging workers what the 95% confidence interval numbers mean. Include your
    Excel output.  Is there anything you
    would want to note for management?

B.
Use the same dataset you used for the
previous problem.  Over a period of time,
Juan determines that the true mean of the packages is in fact 1.72 ounces with
standard deviation the same as the sample above. Assume that Juan has a strong
consumer orientation. Juan is also a savvy businessman. Indeed, a local TV
station has been checking up on Juan by periodically sampling 36 packages and
figuring up the average weight. Juan tells you that he wants to be at least 95%
sure that the average package has at least 1.7 ounces. Further, he wants to be
sure that 95% of the time, the TV crew that is watching him will find a sample
mean of at least 1.70 ounces. At the same time he doesn’t want to set the equipment
to fill packages with any more product than he absolutely has to. What advice
would you give the mustard seed packaging factory management as to how to
calibrate their equipment? In particular, should they increase or decrease the
amount they are putting in the packages and by how much? Are there any other
steps they might be able to take to improve the situation?

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