You want to obtain a sample to estimate a population mean. Based on previous evidence, youbelieve the population standard deviation is approximately o = 70.4. You would like to be 99.5%confident that your esimate is within 2 of the true population mean. How large of a sample size isrequired?n =Do not round mid-calculation. However, use a critical value accurate to three decimal places – thisis important for the system to be able to give hints for incorrect answers.

Name: You want to obtain a sample to estimate a population mean. Based on p
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Description: You want to obtain a sample to estimate a population mean. Based on previous evidence, youbelieve the population standard deviation is approximately o = 70.4. You would like to be 99.5%confident that your esimate is within 2 of the true population m

Answered: You want to obtain a sample to estimate…

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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You want to obtain a sample to estimate a population mean. Based on previous evidence, you
believe the population standard deviation is approximately o = 70.4. You would like to be 99.5%
confident that your esimate is within 2 of the true population mean. How large of a sample size is
required?
n =
Do not round mid-calculation. However, use a critical value accurate to three decimal places – this
is important for the system to be able to give hints for incorrect answers.

Expert Solution

Step 1

Given: Population SD, $σ = 70.4$

Level of significance, $α = 0.005$

The margin of error, E = 2

We know that

The margin of error is given by

$E = Z_{α / 2} \times \frac{σ}{\sqrt{n}}$

=> $n = {(\frac{Z_{α / 2} \times σ}{E})}^{2}$

=> $n = {(\frac{2.805 \times 70.4}{2})}^{2}$

=> n = 9748.797 ~ 9749

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