Answer:
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%
[tex]\hat{p} = 0.48[/tex]
We have to construct a 95% confidence interval.
Margin of error = 2% = 0.02
Formula for margin of error =
[tex]z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
Putting values, we get,
[tex]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[/tex]
Thus, around 2397 Americans must be surveyed to get a margin of error of 2%.
