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

Question

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.

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

Probability that approval rating is within two standards error corressponds to a z-score of -2

For a z-score of -2

P(Z>-2) = 97.5%

There is a 0.975 chance that approval rating is within 2 standard errors.

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