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The size of the sample used is 81
The sample size is a part of the population sample used in an empirical study to make a statistical judgment.
From the parameters given:
The level of significance ∝ = 1 - C.I
∝ = 1 - 0.90
∝ = 0.10
From the [tex]\mathbf{Z_{\alpha /2}}[/tex] tables:
[tex]= \mathbf{Z_{0.10/2} = \mathbf{Z_{0.05} = 1.64}}[/tex]
We are given the lower limit and the upper limit of the population proportion to be: (0.4086, 0.5914)
The sample proportion is:
[tex]\mathbf{\hat p = \dfrac{lower \ limit + upper \ limit }{2}}[/tex]
[tex]\mathbf{\hat p = \dfrac{0.4086 + 0.5914 }{2}}[/tex]
[tex]\mathbf{\hat p = \dfrac{1}{2}}[/tex]
[tex]\mathbf{\hat p =0.5}[/tex]
The size of the sample(n) can be determined by using the margin of error formula:
i.e.
[tex]\mathbf{M.O.E = Z_{\alpha/2} \sqrt{\dfrac{\hat p ( 1 - \hat p)}{n}}}}[/tex]
where;
[tex]\mathbf{0.0914 = 1.645 \sqrt{\dfrac{0.5 ( 1 -0.5)}{n}}}}[/tex]
[tex]\mathbf{n= {\dfrac{1.645^2 \times 0.5^2}{0.0914^2}}}}[/tex]
n = 80.98
n ≅ 81
Learn more about sample size (n) here:
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