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Georgia [21]
3 years ago
12

Legalize Marijuana, Part II. As discussed in Exercise 6.12, the 2010 General Social Survey reported a sample where about 48% of

US residents thought marijuana should be made legal. If we wanted to limit the margin of error of a 95% confidence interval to 2%, about how many Americans would we need to survey
Mathematics
1 answer:
kvv77 [185]3 years ago
8 0

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

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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