The amount of contaminants that are allowed in food products is determined by th

Question

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 118000 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 781437 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. standard deviation of the sampling distribution =18657.44

b. probability that a simple random sample of 40 1 cc specimens has a mean of at least 781437 pus cells = 0.0460

Assiignment: Explain the results above and use them to make an argument that the assumed population mean is incorrect. Structure your essay as follows:

1. Describe the population and parameter for this situation.

2. Describe the sample and statistic for this situation.

3. Give a brief explanation of what a sampling distribution is.

4. Describe the sampling distribution for this situation.

5. Explain why the Central Limit Theorem applies in this situation.

6. Interperet part b.

7. Because part b is unusual (less than 5% probability) determine if the assumed population mean is either correct or incorrect. If incorrect, indicate whether you think the actual population mean is greater or less than the assumed value.

8. Explain what the FDA should do with this information.

Explanation / Answer

We are allowed to do 4 subparts question at a time. Post again for more subparts of question.

a) Cow milk is the population and parameter is

cells = 750000

SD = 118000

b) sample = 40 specimens of 1cc

Mean = 781437

c) A sampling distribution is a probability distributionof a statistic obtained through a large number of samples drawn from a specific population. Thesampling distribution of a given population is thedistribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.

d) For this situation sampling distribution is normal

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