Answer: 18
Step-by-step explanation:
The formula to find the minimum sample size is given by :_
[tex]n=(\dfrac{z^*\cdot \sigma}{E})^2[/tex]
, where [tex]\sigma[/tex] = population standard deviation.
z*= critical z-value.
E= Margin of error.
Given : [tex]\sigma= 13[/tex]
E= ± 8
We know that critical value corresponding to 99% confidence level = z*=2.576 [Using z-table]
Then, the required sample size would be :
[tex]n=(\dfrac{(2.576)\cdot (13)}{8})^2[/tex]
[tex]\Rightarrow\ n=(4.186)^2[/tex]
[tex]\Rightarrow\ n=17.522596\approx18[/tex] [Round to next integer.]
Hence, the required minimum sample size = 18
