The article “The Soundtrack of Recklessness: Musical Preferences and Reckless Behavior Among Adolescents” (Journal of Adolescent Research [1992]: 313–331) described a study whose purpose was to determine whether adolescents who preferred certain types of music reported higher rates of reckless behaviors, such as speeding, drug use, shoplifting, and unprotected sex. Independently chosen random samples were selected from each of four groups of students with different musical preferences at a large high school: (1) Acoustic/pop, (2) Mainstream rock, (3) Hard rock, (4) Heavy metal. 

Each student in these samples was asked how many times he or she had engaged in various reckless activities during the last year. The following table lists data and summary quantities on driving over 80 mph that is consistent with summary quantities given in the article (the sample sizes in the article were much larger, but for the purposes of this exercise, we use n₁ = n₂ = n₃ = n₄ = 20):

Also, N = 80, grand total = 230.0, and

Carry out an F test to determine if these data provide convincing evidence that the true mean number of times driving over 80 mph varies with musical preference.

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n X S 5² Number of Times Driving Over 80 mph by Musical Preference Main- Acoustic/ stream Rock Pop 23413 3NN-33 تا دم درا دم درا درا نا نا نا نا نا نا نا نا نا نا - 3 3 2 2 2 2 2 2 3 4 20 2.50 .827 .6839 32123 ISINGEN- 4 4 2 3 2 3 3 20 2.70 .979 .9584 Hard Rock 3 143NI4NNM MAMMA MING 2 2 2 2 3 4 3 2 3 4 2 4 20 2.75 .967 .9351 Heavy Metal 4 343 m m m SATIS 3 3 3 2 4 4 5 4 5 4 5422 3 20 3.55 .887 .7868