Question

A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken if the grower wishes to estimate the proportion of his trees that are infected with citrus red mite to within 0.08 with probability 0.9?

Answer 1

Answer: 68

Explanation:

Formula for sample size when prior estimate of population proportion (p) is available:
`n=p(1-p)((z^*)/(E))^2`

, 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

`p=(1)/(5)=0.2`

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 :
`n=(0.2)(1-0.2)(((1.645))/(0.08))^2`

`\Rightarrow\ n=(0.2)(0.8)(20.5625)^2`

`\Rightarrow\ n=0.16(422.81640625)\\\\\Rightarrow\ n=67.650625\approx68` [Rounded to next integer.]

Thus, the minimum sample size should be taken =68