Question

You want to estimate the population proportion of pine trees over 90 years old in a forest near where you live. You need a margin of error of no more than 2%. With no more information to go on, what's the simplest formula for calculating your minimum sample size?

n equals open parentheses fraction numerator z asterisk times over denominator m end fraction close parentheses squared bullet P to the power of asterisk times open parentheses 1 minus P to the power of asterisk times close parenthesesA.

a. n equals open parentheses fraction numerator t asterisk times over denominator 2 m end fraction close parentheses squaredB.
b. n equals open parentheses fraction numerator z asterisk times over denominator m end fraction close parentheses squared bullet P open parentheses 1 minus P close parenthesesC.
c. n equals open parentheses fraction numerator z asterisk times over denominator 2 m end fraction close parentheses squaredD.
d. Can't Be Determined E.

Answer 1

b

Explanation:

Minimum sample size for estimating the population proportion of pine trees over 90 years old in a forest near where you live with margin of error no more than 2% can be calculated using the equation:

n≥ p×(1-p) ×
`((z)/(ME) )^2` where

• n is the sample size

• p is the proportion of pine trees over 90 years old in a forest near where you live

• z is the corresponding z-score for the confidence level

• ME is the margin of error in the estimation (2% or 0.02)