QUESTION 2I want to conduct a survey to find who is going to win the election for governor in various states. For the same confidence level and same margin oferror, if I survey Florida (pop. approx. 20 million) and Montana (pop. approx. 1 million), which of the following is true?O I will have to interview more people in Montana because they live farther apart.O I will have to interview 20x more people in Florida because more people live there.O I can interview the same number of people from each state.O I can't use a simple random sample because the situation is too complicated.

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Description: QUESTION 2I want to conduct a survey to find who is going to win the election for governor in various states. For the same confidence level and same margin oferror, if I survey Florida (pop. approx. 20 million) and Montana (pop. approx. 1 million),

Answered: I want to conduct a survey to find who…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Step 1

For the same confidence level and the same margin of error, we must have the number of people sampled from Florida and Montana being the same.

The margin of error is given as:

$C r i t i c a l v a l u e_{α} \times S E$

$w h e r e S E = \frac{σ}{\sqrt{n}}$

Step 2

From the problem,

$\begin{array}{rcl} M a r g i n o f e r r o r_{F l o r i d a} & = & M a r g i n o f e r r o r_{M o n \tan a} \\ \Rightarrow & C r i t i c a l v a l u e_{α} \times S E_{F l o r i d a} = C r i t i c a l v a l u e_{α} \times S E_{M o n \tan a} \\ \Rightarrow & S E_{F l o r i d a} = S E_{M o n \tan a} \\ \Rightarrow & \frac{σ_{F l o r i d a}}{n_{F l o r i d a}} = \frac{σ_{M o n \tan a}}{n_{m o n \tan a}} \end{array}$

Assuming equal variances for the two states we have:

$n_{F l o r i d a} = n_{M o n \tan a}$

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