Question

A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard deviation of 1.07 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.4 liter when constructing a 99% confidence interval?

Answer 1

Solution :

Given that,

standard deviation =s =   =1.07

Margin of error = E = 0.4

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58 ( Using z table ( see the 0.005 value in standard normal (z) table corresponding z value is 2.58 )  

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

n = ( 2.58* 1.07 / 0.4 )2

n =47.63

Sample size = n =48