For each of the following hypothesis testing scenarios, indicate whether or not the appropriate hypothesis test would be for a difference in population means. If not, explain why not.
Scenario 1: The authors of the paper “Adolescents and MP3 Players: Too Many Risks, Too Few Precautions” (Pediatrics [2009]: e953–e958) studied independent random samples of 764 Dutch boys and 748 Dutch girls ages 12 to 19. Of the boys, 397 reported that they almost always listen to music at a high volume setting. Of the girls, 331 reported listening to music at a high volume setting. You would like to determine if there is convincing evidence that the proportion of Dutch boys who listen to music at high volume is greater than this proportion for Dutch girls. Scenario 2: The report “Highest Paying Jobs for 2009– 10 Bachelor’s Degree Graduates” (National Association of Colleges and Employers, February 2010) states that the mean yearly salary offer for students graduating with accounting degrees in 2010 is $ 48,722. A random sample of 50 accounting graduates at a large university resulted in a mean offer of $ 49,850 and a standard deviation of $ 3,300. You would like to determine if there is strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the 2010 national average of $ 48,722. Scenario 3: Each person in a random sample of 228 male teenagers and a random sample of 306 female teen-agers was asked how many hours he or she spent online in a typical week (Ipsos, January 25, 2006). The sample mean and standard deviation were 15.1 hours and 11.4 hours for males and 14.1 and 11.8 for females. You would like to determine if there is convincing evidence that the mean number of hours spent online in a typical week is greater for male teenagers than for female teenagers.