Answer:
The minimum sample size 'n' = 862.538
Step-by-step explanation:
<u><em> Step(i)</em></u>:-
Given the percentage of students favoring a four-day school week during May and June of every school year is approximately 85%
Given the Proportion of students favoring a four-day school week during May and June of every school year
p = 85% = 0.85
q = 1-p = 1-0.85 = 0.15
Given Margin of error = 2 % or 0.02
Level of significance = 0.90 or 0.10
The critical value Z₀.₁₀ = 1.645
<u><em>Step(ii)</em></u>:-
The Margin of error is determined by
![0.02=1.645 X \sqrt{\frac{0.85(0.15)}{n} }](https://tex.z-dn.net/?f=0.02%3D1.645%20X%20%5Csqrt%7B%5Cfrac%7B0.85%280.15%29%7D%7Bn%7D%20%7D)
Cross Multiplication, we get
![\sqrt{n} =1.645 X {\frac{\sqrt{0.125} )}{0.02} }](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D1.645%20X%20%7B%5Cfrac%7B%5Csqrt%7B0.125%7D%20%29%7D%7B0.02%7D%20%7D)
√n = 29.369
squaring on both sides, we get
n = 862.538
<u><em>Final answer:</em></u>-
<em>Sample size 'n' = 862.538</em>
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