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, theindividuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.Hours of SleepFewer than 66 to 6.97 to 7.98 or more39 or younger 40 or older405877Age Group6538557592(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 mutually exclusive from age.H₂: Hours of sleep per night is not mutually exclusive from age.O Ho: Hours of sleep per night is independent of age.H₂: Hours of sleep per night is not independent of age.O Ho: Hours of sleep per night is not independent of age.H₂: 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.H₂: 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 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 cannot conclude that hours of sleep per night and age are independent.O 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 7.9 hours, and hours or more per night? Round your answers to 1 decimal place.Fewer than 6%6 to 6.9%7 to 7.9%8 or more%

a)It is needed to check whether hours of sleep are independent of age.

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. Hours of Sleep Fewer than 6 6 to 6.9 7 to 7.9 8 or more Age Group 39 or younger 40 or older 38 40 58 77 65 55 75 92 (a) Conduct a test of independence to determine whether hours of sleep are independent of age. State the null and alternative hypotheses. OH: Hours of sleep per night is mutually exclusive from age. H: Hours of sleep per night is not mutually exclusive from age. OH: Hours of sleep per night is independent of age. H:Hours of sleep per night is not independent of age. OH: Hours of sleep per night is not independent of age. H: Hours of sleep per night is independent of age. OH: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups. H: 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.) D-value-[ Using a 0.05 level of significance, what is your conclusion? O Reject H. We conclude that hours of sleep per night and age are independent. O Do not reject H. We cannot conclude that hours of sleep per night and age are not independent. O Do not reject H.. We cannot conclude that hours of sleep per night and age are independent. O Reject H. 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 7.9 hours, and 8 hours or more per night? Round your answers to 1 decimal place. Fewer than 6 6 to 6.9 7 to 7.9 8 or more