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posted by  T4RMINAT3R on 10/17/2009 8:10:49 PM  |  status: Closed  |  Earned Karma: 50

Probability Distributions

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Statistics and Probability N/A N/A N/A 10/18/2009 at 9:00:00 PM
Question Details:
Eurobarometer has tracked opinions of Europeans about the common currency ( the euro ) now used in many European countries. When it was introduced in January 2002, 67% of adult resident of the affected countried indicated they were happy that the euro had arrived. Suppose a poll of size 1000 is planned next year to estimate the percentage of people who now approve the common currency. Suppose the population proportion equals .67.

a) With a random sample, explain why it is reasonable to use the binomial for the probability distribution of the number of the 1000 who will indicate approval of the euro. For the bionomial, what is the n and what is p?

b) Find the mean and standard deviation of the probality distribution in (a)

c) Suppose the poll is taken and that 800 people indicate approval. Does this give strong evidence that the percentage approiving of the euro has gone up? Explain
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posted by Jonpp on 10/17/2009 8:26:35 PM  |  status: Live
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Response Details:
(a) Since this sample is matched the assumptions of the binomial distribution, it is reasonable to use the binomial for the probability distribution of the number of the 1000 who will indicate approval of the euro.


Binomial distribution with n=1000, p=0.67.


(b) the mean is n*p=1000*0.67=670
the standard deviation is √1000*0.67*(1-0.67)=14.87


(c) Since p=800/1000=0.8 >0.67, this gives strong evidence that the percentage approiving of the euro has gone up.
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