The amount of contaminants that are allowed in food products is determined by the FDA (Food and Drug Administration). Common contaminants in cow milk include feces, blood, hormones, and antibiotics. Suppose you work for the FDA and are told that the current amount of somatic cells (common name "pus") in 1 cc of cow milk is currently 750,000 (note: this is the actual allowed amount in the US!). You are also told the standard deviation is 59000 cells. The FDA then tasks you with checking to see if this is accurate. You collect a random sample of 40 specimens (1 cc each) which results in a sample mean of 767410 pus cells. Use this sample data to create a sampling distribution. Assume that the population mean is equal to the FDA's legal limit and see what the probability is for getting your random sample. a. Why is the sampling distribution approximately normal? b. What is the mean of the sampling distribution? c. What is the standard deviation of the sampling distribution? d. Assuming that the population mean is 750,000, what is the probability that a simple random sample of 40 1 cc specimens has a mean of at least 767410 pus cells? e. Is this unusual? Use the rule of thumb that events with probability less than 5% are considered unusual. Yes or No? f. Explain your results above and use them to make an argument that the assumed population mean is incorrect.
Applying the Central Limit Theorem:
The amount of contaminants that are allowed in food products is determined by the FDA (Food and Drug Administration). Common contaminants in cow milk include feces, blood, hormones, and antibiotics. Suppose you work for the FDA and are told that the current amount of somatic cells (common name "pus") in 1 cc of cow milk is currently 750,000 (note: this is the actual allowed amount in the US!). You are also told the standard deviation is 59000 cells. The FDA then tasks you with checking to see if this is accurate.
You collect a random sample of 40 specimens (1 cc each) which results in a sample
a. Why is the sampling distribution approximately normal?
b. What is the mean of the sampling distribution?
c. What is the standard deviation of the sampling distribution?
d. Assuming that the population mean is 750,000, what is the probability that a simple random sample of 40 1 cc specimens has a mean of at least 767410 pus cells?
e. Is this unusual? Use the rule of thumb that
f. Explain your results above and use them to make an argument that the assumed population mean is incorrect.
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