Statistics and R problem Please answer These problems as much as possible, thank

Question

Statistics and R problem

Please answer These problems as much as possible, thanks!

14. During the 2010 census, the population of Stillwater, OK, was 46,048. Only 432 of this group knows the official state beverage. If one randomly calls 1000 people in Stillwater,

1.what is the probability that none of them knows the official state beverage?

•2.What data-collection scheme would produce the Binomial result?

•3.What data-collection scheme would produce the Hypergeometric result?

4. Solve this problem both as a Binomial problem and as a Hypergeometric problem. Comment on the difference in probability estimates between the two data-collection schemes.

Explanation / Answer

Probability of knowing theofficial state beverage (p) =432/46048 = 0.009382

Randomly calls 1000 people.

Probability that none of them knows the official state beverage = (1-0.009382)^1000=0

If randomly make 1000 calls , ignorning the previous call whether made to a particular person or not then this produces binomial results. in simple words probability of knowing the state beverage in each call is equal and all the trials are independent then this results binomial result.

3. If we omit the calls that are already made from the population and make calls then it results hyper geometric

4. In 1000 trails , none of them knows the official stage beverage = (1000C0) (0.9906)^1000 (0.0094)^0 = 0

In hyper geometric case , = (432C0)(45616C1000)/(46048C1000) = 0.000037

There is very minute difference between due to the large population size

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