Question

The amount of contaminants that are allowed in food products is determined by the FDA (Food & Drug Administration). Common contaminants in cow milk includes feces, blood, hormones and antibiotics. The current amount of somatic cells (common name “pus”) allowed in 1 cc of cow milk is currently set at 750,000. (Note This is the actual amount currently allowed in the US!) The standard deviation is 67,000 cells. The FDA then tasks you with checking to see if this is accurate.  

You collect a random sample of 45 specimens (1 cc each) which results in a sample mean of 767,722 pus cells.  

1.Does the sample mean fall to the LEFT or the RIGHT of the actual mean?

2.How many standard deviations away from the true mean would a sample mean of 767,722 fall?

3.

Draw or Create a graph with a normal curve that illustrates the probability of the sample mean having at least 767,722 pus cells.

For this graph you must include the following:

true mean (i.e. population mean)

mean of random sample

shade applicable area under the curve

label/indicate the size of the shaded area, as a percentage

4.

Explain in detail what your results mean in context of this problem (i.e. the mean of the sample and how it compares to the actual mean).

Using your response as to whether or not you consider the results unusual, what could you assume in regards to the population mean? Do you think it is correct or incorrect? Why? If incorrect, do you think the actual population mean is greater or less?  

What do you think the FDA should do with this information ?

Answer 1

a) RIght of the actual mean because sample mean is higher than actual mean.

b)

1.77437 standard deviations away from the true mean would a sample mean of 767,722 fall.

c) Standard error:

4) The probability of event is less than 0.05. Using event probability we can consider it as Unusual event.

To be usual value; Z score must be <1.645. So, we can consider actual population mean is less than sample mean.

We conclude that the test statistic is significant and there is sufficient evidencet that the sample mean is higher than actual population mean.