Question

A toy manufacturer wants to know how many new toys children buy each year. Assume a previous study found the variance to be 3.61. She thinks the mean is 9.3 toys per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.12 at the 90% level of confidence? Round your answer up to the next integer.

Answer 1

Solution :

Given that,

standard deviation =   =3.61=1.9

Margin of error = E = 0.12

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )  

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

n = ( 1.645 *1.9 / 0.12 )2

n =678.38

Sample size = n =678