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

Question Description

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?



Final Answer

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