Question

An article describes a method of analyzing digital music files to determine the key in which the music is written. In a sample of 340 classical music selections, the key was identified correctly in 293 of them. How many music pieces should be sampled to specify the proportion to within ±0.025 with 90% confidence? Round the answer to the next integer.

Answer 1

Solution:

Given that,

n = 340

x = 293

= x /n = 293 / 340 = 0.862

1 - = 1 - 0.862 = 0.138

margin of error = E = 0.025

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= (1.645 / 0.025)² * 0.862 * 0.138

= 462.64

= 463

n = sample size = 463