A survey was conducted 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. Age Group 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. State the null and alternative hypotheses. O Ho: Hours of sleep per night is independent of age. Ha: Hours of sleep per night is not independent of age. O Ho: Hours of sleep per night is mutually exclusive from age. Ha: Hours of sleep per night is not mutually exclusive from age. O Ho: Hours of sleep per night is not independent of age. Ha: Hours of sleep per night is independent of age. O Ho: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups. Ha: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups. Find the value of the test statistic. (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = Using a 0.05 level of significance, what is your conclusion? O Reject Ho. We conclude that hours of sleep per night and age are not independent. O Reject Ho. We cannot conclude that hours of sleep per night and age are not independent. O Do not reject Ho. We cannot conclude that hours of sleep per night and age are not independent. O Do not reject Ho. We conclude that hours of sleep per night and age are not independent.(b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 19 hours, and 8 hours or more per night