Assume That Two Presidential Candidates, Call Them Bush and Gore $\hat { p }$

question 39

Essay

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 $\hat { p }$ be the fraction of successes (1s)in a sample, which is distributed N(p, $\frac { p ( 1 - p ) } { n }$ )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 $\hat { p }$ ? 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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Definitions:

Appetite-Suppressing

Related to or having the ability to reduce the desire to eat, often used in the context of diet and weight loss.

Hypothalamus

A region of the brain below the thalamus, responsible for regulating many vital bodily functions including hunger, thirst, temperature, and emotional responses.

Basal Metabolic Rate

The rate at which the body uses energy while at rest to maintain vital functions such as breathing and keeping warm.

Blood Glucose Levels

The concentration of glucose in the blood, which is a critical aspect of metabolic health and energy production.