Answer: 68
Step-by-step explanation:
Formula for sample size when prior estimate of population proportion (p) is available: [tex]n=p(1-p)(\dfrac{z^*}{E})^2[/tex]
, where z*= critical-value.
E= Margin of error.
Let p be the population proportion of trees are infected with the citrus red mite.
As per given , we have
[tex]p=\dfrac{1}{5}=0.2[/tex]
E= ± 0.08
The critical z-value corresponding to 90% confidence level = z*=1.645
Substitute all the values in the above formula , we get
Required sample size :[tex]n=(0.2)(1-0.2)(\dfrac{(1.645)}{0.08})^2[/tex]
[tex]\Rightarrow\ n=(0.2)(0.8)(20.5625)^2[/tex]
[tex]\Rightarrow\ n=0.16(422.81640625)\\\\\Rightarrow\ n=67.650625\approx68[/tex] [Rounded to next integer.]
Thus, the minimum sample size should be taken =68
