There is a proposal before Congress to build a so-called fourth-generation nuclear reactor at the Idaho National Laboratory. Government officials want to estimate the true proportion of citizens in the state who support building the reactor. The most recent survey on Idaho public opinion about building nuclear reactors showed 40% in favor. If the government officials want a margin of error of 4% and a confidence level of 90%, how many voters will they need to survey?

Question

Mathematics

Lorenzo Bowman

24 September, 14:45

There is a proposal before Congress to build a so-called fourth-generation nuclear reactor at the Idaho National Laboratory. Government officials want to estimate the true proportion of citizens in the state who support building the reactor. The most recent survey on Idaho public opinion about building nuclear reactors showed 40% in favor. If the government officials want a margin of error of 4% and a confidence level of 90%, how many voters will they need to survey?

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Answers (1)

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Diamond · Answer 1

406

Step-by-step explanation:

Data provided in the question:

Margin of error, E = 4% = 0.04

Probability of people in favor, p = 40% = 0.4

Confidence level = 90%

Now,

For 90% confidence level, the z value = 1.645

let n be the required sample size

Thus,

n = p (1 - p) (z : E) ²

or

n = 0.4 * (1 - 0.4) (1.645 : 0.04) ²

or

n = 0.4 * 0.6 * 1691.265625

or

n = 405.90 ≈ 406