Question

A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested to estimate this proportion to within 0.06 with 95% confidence?

Answer 1

Solution :

Given that,

= 0.5 ( use 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E =0.06

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.06)2 * 0.5 * 0.5

= 266.777

Sample size =267