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 113000 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 773070 pus cells. Use this sample data to create a sampling distribution.
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 55 1 cc specimens has a
mean of at least 773070 pus cells?
e. Is this unusual? Use the rule of thumb that events with
probability less than 5% are considered unusual.
f. Explain your results above and use them to make an argument that
the assumed population mean is incorrect. (6 points) Structure your
essay as follows:
a). Because our sample size is greater than 30, the Central limit theorem tells us that the sampling distribution will approximately normally a normal distributed. Because we know the population standard deviation and sample size is large, now we will use normal distribution to find probability.
b). Size,n= 55,. mean of sample xbar= 773070
c). Standard deviation sigma= 113000/55= 2055
d). Probability of sample mean at least 773070 is approximately zero
Applying the Central Limit Theorem: The amount of contaminants that are allowed in food products is...
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...
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...
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...
The Central Limit Theorem is important in statistics because _. A for a large n, it says the population is approximately normal B for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size C for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the population D for any size sample, it says the sampling distribution of the sample mean is approximately...
ORMAL CURVES AND SAMPLING DİSTRIBUTIONS Basic Computation: Central Limit Theorem Suppose x has a distributi on with a mean of 20 and a standard deviation of 3. Random samples of size n are drawn. (a) Describe the a distribution and compute the mean and standard deviation of the distribution. (b) Find the z value corresponding to x = 19. (c) Find Pr < 19) (d) Interpretation Would it be unusual for a random sample of size 36 from the x...
Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. The mean price of photo printers on a website is $243 with a standard deviation of $59. Random samples of size 26 are drawn from this population and the mean of each sample is determined. The mean of the distribution of sample means is _______.
Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. The mean price of photo printers on a website is $240 with a standard deviation of $60. Random samples of size 35 are drawn from this population and the mean of each sample is determined.
The central limit theorem states that if a random and representative sample from a population contains more than 15 observations the sampling distribution of the sample mean will be approximately normal
Choose all that are true about the central limit theorem a. sample size is important when the population is not normally distributed b. the sampling distribution of the sample means will be skewed positively or negatively c. the sampling distribution of the sample means is approximately normally distributed d. the population mean and the mean of all sample means are equal PLEASE DO NOT ANSWER IF YOU DO NOT KNOW. I need to learn from these questions that I do...
True or False: the central limit theorem states that the sampling distribution of the sample mean is approximately normal whenever the population from which we are sampling is normally distributed Assume that 14% of the items produced in an assembly line operation are defective, but that the firm’s production manager is not aware of this situation. Assume firtber that the wuality assurance department to determine the quality of the assembly operation tests 50 parts. What is the probability that the...