Question

Im not sure how to work part f. I do not need any of the other answers. They're already completed. Can anyone please help with partt F (1-8)?

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 148000 cells. The FDA then tasks you with checking to see if this is accurate. You collect a random sample of 55 specimens (1 cc each) which results in a sample mean of 782258 pus cells. Use this sample data to create a sampling distribution.

a. Why is the sampling distribution approximately normal? sample size is large enough for the population mean (55 to be exact)

b. What is the mean of the sampling distribution? 750,000

c. What is the standard deviation of the sampling distribution? 19956.32

d. Assuming that the population mean is 750,000, what is the probability that a simple random sample of 55 1 cc specimens has a mean of at least 782258 pus cells? .0530 e. Is this unusual? Use the rule of thumb that events with probability less than 5% are considered unusual. No or Yes ? No since it's 5.3%

f. Explain your results above and use them to make an argument that the assumed population mean is incorrect. Structure your essay as follows: (1-8)

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. Interpret the answer to part d.

7. Use the answer to part e. to argue that 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.

Answer 1

f) 1) here the population is the entire set of cow milk that has been prodcued. and the parameter is the mean amount of somatic cells in the entire population.

2) The sample is the random sample of 55 specimens that has been collected and statistic is the sample mean amount of somatic cells

3) The sampling distribution is the distribution of statistic generated out of the random sample collected. Because the sample collected from the population is random, so statistic of the sample will be also random, and that will vary according to the sample that is chosen. So, the probability distribution which statistic follows is strictly determined by the probability that the particular random sample is collected.

4) In this situation, the statistic is sample mean and by central limit theorem, the approximate distribution of sample mean will be Normal.

5) Because, each of the 55 specimen is independently chosen and 55 > 30, there is enough sample size, central limit theorem applies here.

6) The approximate probability that for a random sample from the above population, the sample mean comes atleast 782258 is 5.3%, which is very marginal, i.e the probability is very low. There is a hint that the actual population mean(which we don't know) might be shifted to greater than  750000.

7) Well, it is completely dependent on the tolerance level. If the tolerance level is 10%, then 5.3% < 10%, so it is incorrect, it the tolerance is 5% then it is correct, but still, it is very marginal. One should not come to a direct conclusion here.

8) The FDA should collect another sample possibly of higher size(to gather more info) and do the same calcuation and infer from that.