# Essay Question

#### SamSch

##### New Member
Hello all,

I have to write an essay at the moment and unfortunately I am stuck on a question, maybe you can help me with it.

The question is as follows: "Describe in your own words how an approximation method that determines a confidence interval for the mean of a population from a sample can be derived from the urn model. Also state a necessary requirement."

Unfortunately, I can't find any literature for this question. I believe this question is not too complicated, but unfortunately I am a little bit lost.

Maybe you guys can help me out!

Thanks and many greetings
Sam

#### Buckeye

##### Active Member
It seems like your question has missing detail that may help us. Can you elaborate on the "urn" model? Are there details prior to the essay question?

#### SamSch

##### New Member
It seems like your question has missing detail that may help us. Can you elaborate on the "urn" model? Are there details prior to the essay question?
Unfortunately, this is the question with which the paper begins. The hypergeometric distribution is the main chapter. "To describe the distribution, a so-called urn model is used. An urn is in this context a container, in which well mixed N balls are. N different balls are drawn without putting them back, and their colors are noted." At least that's what it says in the script of the course. I cant quite get my head around what the urn model has to do with the approximations methods and confidence interval. I also have the feeling that information is missing, but the instructor is currently unavailable and I would like to solve the problem #### Buckeye

##### Active Member
Well, this paper might be of some help. http://www.wright.edu/~weizhen.wang/paper/37-2015jasa_wang.pdf
The question as stated leaves room for interpretation. If they are asking about a mean, then I make an assumption it is the mean number of colored marbles from the urn. In another scenario, we can represent the colored marbles as a proportion of total marbles in the urn.

#### SamSch

##### New Member
Well, this paper might be of some help. http://www.wright.edu/~weizhen.wang/paper/37-2015jasa_wang.pdf
The question as stated leaves room for interpretation. If they are asking about a mean, then I make an assumption it is the mean number of colored marbles from the urn. In another scenario, we can represent the colored marbles as a proportion of total marbles in the urn.
Thanks a lot for your efforts! I will look into the paper #### max56tyr

##### New Member
I read some articles and can say that it can be used to approximate the mean of a population from a sample. To do this, we draw balls from an urn containing balls of different colors. The proportion of each color in the urn represents the proportion of the population that has each value. For example, if the urn contains 80% red balls and 20% green balls, then we know that the population is predominantly red. We can use this information to calculate a confidence interval for the mean of the population. To do this, we take a sample of balls from the urn and calculate the mean of the sample. We then use the urn model to estimate the distribution of the population. From this, we can calculate a confidence interval forthe population mean. This method is useful when we don't have access to the entire population. it can also be used when the population is too large to use traditional methods. This method is not perfect, but it can give usa good approximation for the mean of a population from a sample.
https://www.ams.org/journals/tran/2004-356-09/S0002-9947-03-03513-X/S0002-9947-03-03513-X.pdf

I will be glad if it will be useful, interesting topic

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