The article “A Music Key Detection Method Based on Pitch Class Distribution Theory describes a method of analyzing digital music files to determine the key in which the music is written. In asample of 335 classical music selections, the key was identified correctly in 293 of them.
a. Find a 90% confidence interval for the proportion of pieces for which the key will be correctly identified.
b. How many music pieces should be sampled to specify the proportion to within ±0.025 with 90% confidence?
c. Another method of key detection is to be tested. At this point, there is no estimate of the proportionof the time this method will be identified correctly. Find a conservative estimate of the sample size needed so that the proportion will be specified to within ±0.03 with 90% confidence.
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