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The article “A Music Key Detection Method Based on Pitch
Chapter 5, Problem 15E(choose chapter or problem)
The article “A Music Key Detection Method Based on Pitch Class Distribution Theory” (J. Sun, H. Li, and L. Ma, International Journal of Knowledge-based and Intelligent Engineering Systems, 2011:165–175) describes a method of analyzing digital music files to determine the key in which the music is written. In a sample 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 \(\pm\)0.025 with 90% confidence?
c. Another method of key detection is to be tested. At this point, there is no estimate of the proportion of 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 \(\pm\)0.03 with 90% confidence.
Equation transcription:
Text transcription:
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Questions & Answers
QUESTION:
The article “A Music Key Detection Method Based on Pitch Class Distribution Theory” (J. Sun, H. Li, and L. Ma, International Journal of Knowledge-based and Intelligent Engineering Systems, 2011:165–175) describes a method of analyzing digital music files to determine the key in which the music is written. In a sample 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 \(\pm\)0.025 with 90% confidence?
c. Another method of key detection is to be tested. At this point, there is no estimate of the proportion of 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 \(\pm\)0.03 with 90% confidence.
Equation transcription:
Text transcription:
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ANSWER:Answer:
Step 1 of 4:
Given in a sample of 335 classical music selections, the key was identified correctly in 293 of them.
Here, n = 335, x = 293.