In a study examining overweight and obese college football players, Mathews and Wagner (2008) found that on average both offensive and defensive linemen exceeded the at-risk criterion for body mass index (BMI). BMI is a ratio of body weight to height squared and is commonly used to classify people as overweight or obese. Any value greater than 30 kg/m2 is considered to be at risk. In the study, a sample of n = 17 offensive linemen averaged M = 34.4 with a standard deviation of s = 4.0. A sample of n = 19 defensive linemen averaged M = 31.9 with s = 3.5.
a. Use a single-sample t test to determine whether the offensive linemen are significantly above the at-risk criterion for BMI. Use a one-tailed test with α = .01.
b. Use a single-sample t test to determine whether the defensive linemen are significantly above the at-risk criterion for BMI. Use a one-tailed test with α = .01.
c. Use an independent-measures t test to determine whether there is a significant difference between the offensive linemen and the defensive linemen. Use a two-tailed test with α = .01.