Question

A grower believes that one in five of his citrus trees are infected with the citrus red mite. What minimum sample should be taken if the grower wishes to estimate the proportion of his trees that are infected with citrus red mite to within 0.05 with a confidence level of 95%? (Round your answer up to the nearest whole number.)

n ≥  trees

Answer 1

Solution:

Given:

p = proportion of citrus trees are infected with the citrus red mite = 1 / 5 = 0.2

E = Margin of Error = 0.05

c = confidence level = 95%

Find sample size n:

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

thus