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Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean and o = 16.6. Assume the population is normally distributed.

Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean and o = 16.6. Assume the population is normally distributed.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean and o = 16.6. Assume the population is normally distributed. A 95% confidence level requires a sample size of (Round up to the nearest whole number as needed.)
Transcribed Image Text:Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean and o = 16.6. Assume the population is normally distributed. A 95% confidence level requires a sample size of (Round up to the nearest whole number as needed.)
Expert Solution
Step 1

The sample size can be calculated as:

n=z×σE2

Here,

z = desired confidence level

E = The allowable margin of error ( sampling error)

σ = Population standard deviation

At a 95% confidence level, the z value is 1.96 which can be obtained by using the standard normal table. 

Given:

z = 1.96 = The value at 95% confidence level

E = 1

σ = 16.6

Substitute the given values in the above-mentioned formula as follows:

n=z×σE2=1.96· 16.612=1058.591≃1059

 

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