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We saw that if we want to have a probability of at least 95% that the poll results are within 1 percentage point of the truth, Chebyshev's inequality recommends a sample size of n=50,000 . This is very large compared to what is done in practice. Newspaper polls use smaller sample sizes for various reasons. For each of the following, decide whether it is a valid reason.
In the real world,
a) the accuracy requirements are looser.
b) the Chebyshev bound is too conservative.
c) the people sampled are all different, so their answers are not identically distributed
d) the people sampled do not have independent opinions.

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Answer:

A. Yes

nowadays the precision requirements are more flexible, it depends largely on the variability

B. Yes

this limit is very conservative to give the probability that the population parameter is within that confidence interval,

C. No

the people in the sample are not without common variables and therefore their responses will be identically distributed

D. No

the people in the sample will have independent opinions, because it is not a valid argument to reject their point of view

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