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A sample size is the part of the population that helps us to draw inferences about the population. Collecting research of the complete information about the population is not possible and it is time consuming and expensive. Thus, we need appropriate sample size so that we can make inferences about the population based on that sample.
For the equation on how to determine the sample size, please refer to the picture below.
In the problem above, the given are the following:
Confidence level - 99%
Margin of Error (ME) = 0.11
p= 0.35
Unknown: n=?
Solution:
n=p(1-p)z^2 / ME^2
Using your calculator you can get an answer of approximately 125.
The sample size for the given data is 125.
The sample size is defined as the number of observations used for determining the estimations of a given population.
A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values
Let the sample size be n.
According to the given question.
We have
Confidence level = 99%
Margin of error, MOE = 0.11
The z-score, at 99% confidence = 2.58
Since,
[tex]MOE = z\sqrt{\frac{P(1-P)}{n} }[/tex]
Substitute the value of P, z and MOE in the above formula for finding the value of sample size n.
⇒ [tex]0.11=2.58\sqrt{\frac{0.35(1-0.65)}{n} }[/tex]
⇒ [tex]0.11 = 2.58\sqrt{\frac{0.35(0.65)}{n} }[/tex]
⇒ [tex]0.11(2.58)=\sqrt{\frac{0.2275}{n} }[/tex]
⇒ [tex](\frac{0.11}{2.58}) ^{2} =\frac{0.2277}{n}[/tex]
⇒[tex]\frac{121}{665464} = \frac{0.2275}{n}[/tex]
⇒ [tex]n = \frac{15143.31}{121} = 125[/tex]
Hence, the sample size for the given data is 125.
Find out more information about margin of error, sample size, z score and confidence level here:
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