IPods (or iPod Apps on iPhones/iPod's) are incredibly popular for listening to music on the go. The music that you keep on an iPod can be stored in several different formats. Two popular formats are AIFF (Audio Interchange File Format) and AAC (Advanced Audio Coding). Files on an iPod can be in either of these formats, or both. The 596 songs in the Songs. Excel data attached set uses a mixture of these two formats.
A: For each format, create a scatterplot showing the amount of space needed (in MB) for storage based on the length (in seconds) of the song. Comment on what you see in the scatterplots.
B: Create a regression model that can help you estimate the amount of space (in megabytes, MB) that is needed to store a song of a given length (in seconds). The model should be able to estimate the space needed by a song based on its format i.e. given the format, and song length, it should be able to give you an estimate of the amount of space needed.
C. Interpret the R^2, the RMSE, and estimated coefficients (both the intercept term and any slope terms) for your model.
D.Is the space needed per second of song different for the two formats? You need to justify your answer using appropriate statistical reasoning.
E: Create prediction intervals for the amount of space needed in each format for a song that is 3 minutes long.
F) Each song has a random length (in seconds). Assume that the population of songs has some arbitrary distribution with an average song length of 250 seconds, and a standard deviation of 115 seconds. The "population" of songs here describes the total corpus of songs available that people can put on iPods.
i) I have a song collection of 4000 songs. What is the probability that the total play time of my collection (i.e. the total time if all songs in my collection are played once) exceeds 280 hours?
ii) A competitor to Apple wants to produce a compact music player that can hold 4000 songs. It is trying to figure out how many hours of music the player should be able to hold (in order to accommodate 4000 songs). How many hours of music should the player hold to be 95% sure of being able to accommodate a 4000 song collection?