The National Sleep Foundation used a survey to determine whether hours of sleep per night are independent of age. 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.

a. Conduct a test of independence to determine whether hours of sleep are independent of age. Using a .05 level of significance, what is the p-value and what is your conclusion?
b. What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?

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Age Group Hours of Sleep Fewer Than 6 6 to 6.9 7 to 7.9 8 or More 39 or Younger 38 60 40 or Older 36 57 75 92 65