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 53000 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 769495 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. c. What is the standard deviation of the sampling distribution?
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 53000 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 769495 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.
c. What is the standard deviation of the sampling distribution?
The Central Limit Theorem :
Given any random variable X, discrete or continuous, with finite mean µ and finite variance σ2 . Then, regardless of the shape of the population distribution of X, as the sample size n gets larger, the sampling distribution of becomes increasingly closer to normal, with mean µ and variance σ2/n , that is
Where,
- is called the “standard error of the mean,” denoted SEM, or more simply, s.e.
- The corresponding Z-score transformation formula is .
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