Question

Researchers studying trees in the Tobacco Root Mountains wish to estimate the proportion of trees that have been infested by bark beetles. They want to randomly sample trees throughout the forest to estimate this proportion with 90% confidence and a margin of error of 5%.

1.How many trees should they sample? (Hint: use pb = .5)

Is my thinking correct:

n=p^*q^*Z*/ME^2

where p^=o.5, q^=0.5, Z*=1.645 ME^2=0.0025

so 164.5 so answer 165?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 5% = 0.05

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.645 / 0.05)2 * 0.5 * 0.5

=271

Sample size = 271