A random sample of 168 students was asked how many songs were in their digital music library and what fraction of them was legally purchased. Overall, they reported having a total of 117,079 songs, of which 23.1% were legal. The music industry would like a good estimate of the proportion of songs in students’ digital music libraries that are legal.

a) Think carefully. What is the parameter being estimated? What is the population? What is the sample size?

b) Check the conditions for making a confidence interval.

c) Construct a 95% confidence interval for the fraction of legal digital music.

d) Explain what this interval means. Do you believe that you can be this confident about your result? Why or why not?