IDNLearn.com: Your trusted source for accurate and reliable answers. Our platform provides trustworthy answers to help you make informed decisions quickly and easily.
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:
https://brainly.com/question/17203075