The National Sleep Foundation used a survey to determine whether hours of sleep per night are independent of age (Newsweek, January 19, 2004). A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.

Hours of Sleep 39 or younger 40 or Older
Fewer than 6 38 36
6 to 6.9 60 57
7 to 7.9 77 75
8 or more 65 92

a. Conduct a test of independence to determine whether hours of sleep are independent of age. Use α= 0.05 level of significance.
b. What is your conclusion?