Answer:
the minimum sample size n = 11.03
Step-by-step explanation:
Given that:
approximate value of the population standard deviation [tex]\sigma[/tex] = 49
level of significance ∝ = 0.01
population mean = 38
the minimum sample size n = ?
The minimum sample size required can be determined by calculating the margin of error which can be re[resented by the equation ;
Margin of error = [tex]Z_{ \alpha /2}} \times \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]38 = \dfrac{2.576 \times 49}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = \dfrac{2.576 \times 49}{38}[/tex]
[tex]\sqrt{n} = \dfrac{126.224}{38}[/tex]
[tex]\sqrt{n} = 3.321684211[/tex]
[tex]n= (3.321684211)^2[/tex]
n ≅ 11.03
Thus; the minimum sample size n = 11.03
