Question

A random sample of 189 students were asked how many songs were in their digital music library and what fraction of them were legally purchased.​ Overall, they reported having a total of 117,738 ​songs, of which 21.6​% were legal. The music industry would like a good estimate of the percentage of songs in​ students' digital libraries that are legal.

​a)	What is the parameter being​ estimated? What is the​ population? What is the sample​ size?
​b)	Construct a 99​% confidence interval for the fraction of legal digital​ music, if you can. If​ not, explain the problem.

Answer 1

Ansuleni- y (a) The parameter being estimated is the proportion of digital songs in the student's library that are legal. population: all the songs that are held in the digital library Sample size: sample size is the total of 117,738 songs (b) the sample proportion pis proportion of the sample given by P=0.2160 SECA)- B î n 10.2160(1-0.2160) 117,738 -0.000487 The 99% confidence interval for the true proportion p by taking +2.58 SEs from the sample proportion is given by

© +2.58 SECP) 0.2160+ 2.58* 0.0004-87 (0.2160-0.00125,0.2160+0.00125) (0.2147, 0.2172) (21.476%, 21.72460) We are 994% Confidence that betoeen (2114740, 21.72%) of digital songs were legally durchashed. -