Question

A fashion designer wants to know how many new dresses women buy each year. She thinks the mean is 6.6 dresses per year. Assume a previous study found the variance to be 4. How large of a sample would be required in order to estimate the mean number of dresses bought per woman at the 98% confidence level with an error of at most 0.09 dresses?

Answer 1

Solution :

Given that,

variance = ² = 4

standard deviation = = 2

margin of error = E = 0.09

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.33

Sample size = n = ((Z_/2 * ) / E)²

= ((2.33 * 2) /0.09 )²

=2680.93 = 2681

Sample size = 2681