Reference no: EM132372856

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?

n = 3 sample size

m = m  1.72 population mean (mean of sample means)

s = 0.15029 Standard deviation of population

Calculate Standard deviation of sample means (standard error of the mean)

σ   = σ/√n 0.025049

Calculate probability:

P(drawn sample mean < 1.7) = 0.212305

P(drawn sample mean >= 1.7) = 78.8%

The results of the random drawn samples in 78.8% which has a mean equal to or greater than the 1.7 ounces that the mustard seed factory in Colombia will find in the sample mean. This does not meet the expectation of Juan's in wanting to make sure of having 95% of the time and sample mean of at least 1.7 ounces.

I would inform the mustard seed packaging factory management team that they need to calibrate their equipment by adding a bit more mustard seed to each package which can make the distribution to calculate the way they want. By making this change it will guarantee 95% of the time and he sample mean of at least 1.7 ounces. If they do not make the changes the process can get out of hand which can lead to bigger problems until this is fixed.