Eurobarometer has tracked opinions of Europeans about the commoncurrency ( the e

Question

Eurobarometer has tracked opinions of Europeans about the commoncurrency ( the euro ) now used in many European countries. When itwas introduced in January 2002, 67% of adult resident of theaffected countried indicated they were happy that the euro hadarrived. Suppose a poll of size 1000 is planned next year toestimate the percentage of people who now approve the commoncurrency. Suppose the population proportion equals .67.

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

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

c) Suppose the poll is taken and that 800 people indicate approval.Does this give strong evidence that the percentage approiving ofthe euro has gone up? Explain

Explanation / Answer

(a) Since this sample is matched the assumptions of the binomialdistribution, it is reasonable to use the binomial for theprobability distribution of the number of the 1000 who willindicate 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 thatthe percentage approiving of the euro has gone up.

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