Assume that two presidential candidates,call them Bush and Gore,receive 50% of the votes in the population.You can model this situation as a Bernoulli trial,where Y is a random variable with success probability Pr(Y = 1)= p,and where Y = 1 if a person votes for Bush and Y = 0 otherwise.Furthermore,let be the fraction of successes (1s)in a sample,which is distributed N(p, )in reasonably large samples,say for n ≥ 40.
(a)Given your knowledge about the population,find the probability that in a random sample of 40,Bush would receive a share of 40% or less.
(b)How would this situation change with a random sample of 100?
(c)Given your answers in (a)and (b),would you be comfortable to predict what the voting intentions for the entire population are if you did not know p but had polled 10,000 individuals at random and calculated ? Explain.
(d)This result seems to hold whether you poll 10,000 people at random in the Netherlands or the United States,where the former has a population of less than 20 million people,while the United States is 15 times as populous.Why does the population size not come into play?

Question

Assume that two presidential candidates,call them Bush and Gore,receive 50% of the votes in the population.You can model this situation as a Bernoulli trial,where Y is a random variable with success probability Pr(Y = 1)= p,and where Y = 1 if a person votes for Bush and Y = 0 otherwise.Furthermore,let  be the fraction of successes (1s)in a sample,which is distributed N(p,  )in reasonably large samples,say for n ≥ 40.
(a)Given your knowledge about the population,find the probability that in a random sample of 40,Bush would receive a share of 40% or less.
(b)How would this situation change with a random sample of 100?
(c)Given your answers in (a)and (b),would you be comfortable to predict what the voting intentions for the entire population are if you did not know p but had polled 10,000 individuals at random and calculated  ? Explain.
(d)This result seems to hold whether you poll 10,000 people at random in the Netherlands or the United States,where the former has a population of less than 20 million people,while the United States is 15 times as populous.Why does the population size not come into play?

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The Answer of Assume that two presidential candidates,call them Bush and Gore,receive 50% of the votes in the population.You can model this situation as a Bernoulli trial,where Y is a random variable with success probability Pr(Y = 1)= p,and where Y = 1 if a person votes for Bush and Y = 0 otherwise.Furthermore,let  be the fraction of successes (1s)in a sample,which is distributed N(p,  )in reasonably large samples,say for n ≥ 40.
(a)Given your knowledge about the population,find the probability that in a random sample of 40,Bush would receive a share of 40% or less.
(b)How would this situation change with a random sample of 100?
(c)Given your answers in (a)and (b),would you be comfortable to predict what the voting intentions for the entire population are if you did not know p but had polled 10,000 individuals at random and calculated  ? Explain.
(d)This result seems to hold whether you poll 10,000 people at random in the Netherlands or the United States,where the former has a population of less than 20 million people,while the United States is 15 times as populous.Why does the population size not come into play?

Assume That Two Presidential Candidates,call Them Bush and Gore,receive 50