Question

How many M&M candies should be sampled to obtain a 95% confidence interval of the proportion of blue candies with a 4% margin of error if the prior estimate of blueM&M candies is 0.24?

Blue M&M Proportion: 504 total blue, 2523 total m&m's

Answer 1

Solution,

Given that,

= 0.24

1 - = 1 - 0.24 = 0.76

margin of error = E = 4% = 0.04

At 95% confidence level ,

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 / 0.04 )2 * 0.24 * 0.76

= 437.94

Sample size = n = 438