6. A survey is used to quantify the support for an increase in education spendin

Question

6. A survey is used to quantify the support for an increase in education spending. The pollster tells us that the approval rating for the increase is 60% with 4% standard error. Respondents have been modeled with independent identically distributed Bernoulli random variables (a) Approximately how many people did the pollster survey? (b) Even if the true approval rating is 2 standard error away from the pollster's estimate, there would be majority support for the increased spending. What is the lower bound on the probability that approval rating is within 2 standard errors. Hint: use Chebyshev's inequality.

Explanation / Answer

a) Standard error = sqrt(pq/n)

0.04^2 = 0.6*0.4/n

n = 0.24/0.0016= 150

b)Probability than the approval rating is within 2 standard errors is found using chebyshev's inequality as 0.75.

Theory-

In practical usage, in contrast to the 68-95-99.7% rule, which applies to normal distributions, under Chebyshev's inequality a minimum of just 75% of values must lie within two standard deviations of the mean and 89% within three standard deviations.

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