Question

The Queen of Rohan wishes to estimate the mean size of a herd of horses on the plains. She wished to do so by computing a 98% confidence interval with a maximum margin of error of 3. She knows, from past surveys, that the population standard deviation, σ, tended to be 11.3. What is the minimum sample size necessary to compute the described confidence interval?

Answer 1

Solution :

Given that,

standard deviation = =11.3

Margin of error = E = 3

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

sample size = n = [Z/2* / E] 2

n = ( 2.326*11.3 /3 )2

n =76.75

Sample size = n =77