Answer:
-8
Step-by-step explanation:
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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%
![\hat{p} = 0.48](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%20%3D%200.48)
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}}](https://tex.z-dn.net/?f=z_%7Bstat%7D%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D)
![z_{critical}\text{ at}~\alpha_{0.05} = 1.96](https://tex.z-dn.net/?f=z_%7Bcritical%7D%5Ctext%7B%20at%7D~%5Calpha_%7B0.05%7D%20%3D%201.96)
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](https://tex.z-dn.net/?f=0.02%20%3D%201.96%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%5C%5C%5C%5C0.02%20%3D%201.96%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B0.48%281-0.48%29%7D%7Bn%7D%7D%5C%5C%5C%5C%5Csqrt%7Bn%7D%20%3D%201.96%5Ctimes%20%5Cdfrac%7B%5Csqrt%7B0.48%281-0.48%29%7D%7D%7B0.02%7D%5C%5C%5C%5C%5Csqrt%7Bn%7D%3D48.96%5C%5Cn%20%3D%202397.0816%5Capprox%202397)
Thus, around 2397 Americans must be surveyed to get a margin of error of 2%.