Question

What if you wanted a smaller margin of error in your interval for the proportion of left-handed people (say plus or minus 2%)? How many people would you need to survey in order to get a margin of error of 2% ? You can use the LaTeX: \hat{p} p ^ that you already calculated as your estimate in the sample size formula.

Answer 1

Answer:

The sample size n= 2500

A survey with 2500 left-handed people guarantees  the given margin error is 2%

Step-by-step explanation:

Explanation:-

The margin of error = $\frac{2 S.D}{\sqrt{n} }$

here for proportions , the standard deviation (σ) = $\sqrt{p(1-p)} \leq \frac{1}{2}$

$Margin of error = \frac{2 S.D}{\sqrt{n} } \leq \frac{2(\frac{1}{2}) }{\sqrt{n} }$

$Margin of error = \frac{1}{\sqrt{n} }$

now The necessary sample size is

$n= \frac{1}{(M.E)^{2} }$

Given data the survey in order to get a margin of error of 2%

M.E = 0.02

$n= \frac{1}{(0.02)^{2} } = 2500$

Conclusion:-

The sample size n= 2500

A survey with 2500 left-handed people guarantees the given margin error is 2%