Mathematics: Solving equations with variables on both sides

Around 2397 Americans must be surveyed to get a margin of error of 2%.Step-by-step explanation:We are given the following in the question:Proportion of US residents who thinks marijuana should be made legal = 48%We have to construct a 95% confidence interval.Margin of error = 2% = 0.02Formula for margin of error = Putting values, we get,Thus, around 2397 Americans must be surveyed to get a margin of error of 2%....

Solving equations with variables on both sides

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adhanom1271

03.02.2022

Mathematics

Around 2397 Americans must be surveyed to get a margin of error of 2%.

Step-by-step explanation:

We are given the following in the question:

Proportion of US residents who thinks marijuana should be made legal = 48%

$\hat{p} = 0.48$

We have to construct a 95% confidence interval.

Margin of error = 2% = 0.02

Formula for margin of error =

$z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get,

$0.02 = 1.96\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\0.02 = 1.96\times \sqrt{\dfrac{0.48(1-0.48)}{n}}\\\\\sqrt{n} = 1.96\times \dfrac{\sqrt{0.48(1-0.48)}}{0.02}\\\\\sqrt{n}=48.96\\n = 2397.0816\approx 2397$

Thus, around 2397 Americans must be surveyed to get a margin of error of 2%.

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Solving equations with variables on both sides

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