Song Lengths This dataset gives the playing time (in seconds) of a sample of 639 songs grouped by genre (as classified by the online seller).
(a) From your visual inspection of the song lengths, do differences among the average lengths appear large when compared to the variation within genre?
(b) Fit a multiple regression of rating on five dummy variables that represent the blues, country, folk, jazz, and Latin genres. Interpret the estimated intercept and slopes.
(c) Which estimated slope (exclude the intercept) has the smallest standard error? Explain why this standard error is smaller than those of the other slopes.
(d) Does a statistical test agree with your visual impression of the differences among the groups? Test the null hypothesis that the song lengths are the same in the six genres.
(e) The absolute value of the
-statistics of two estimated slopes in the multiple regression is smaller than 2. Why are these estimates relatively close to zero?
(f) A media company recently acquired a station that was playing rock music. The station can work in more ads if the songs it plays are shorter. By changing to another genre, can the company reduce the typical length of songs? Which one(s)?