A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was askedto 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 oryounger and age 40 or older. Sample data follow.Hours of SleepFewer than 66 to 6.97 to 7.98 or moreAge Group39 or younger 40 or olderNeed Help?3862Read It77(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 not independent of age.H₂: Hours of sleep per night is independent of age.a63OHO: 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.%36Ho: 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.)%59What is the p-value? (Round your answer to four decimal places.)p-value =%75Using a 0.05 level of significance, what is your conclusion?Do not reject Ho. We cannot conclude that hours of sleep per night and age are not independent.Do not reject H. We conclude that hours of sleep per night and age are not independent.O Reject H. We conclude that hours of sleep per night and age are not independent.Reject H. We cannot conclude that hours of sleep per night and age are not independent.90(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 8hours or more per night?Fewer than 66 to 6.97 to 7.98 or moreMaster It

The observed frequency table is:Hours of sleepAge Group 39 or youngerAge group 40 or olderTotalfewer…

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 39 or younger 40 or older 7 to 7.9 8 or more 38 62 77 Age Group 63 (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 per night is not independe of age. H: Hours of sleep per night is independent of age. % 36 Ho: Hours of sleep per night is mutually exclusive from age. H: Hours of sleep per night is not mutually exclusive from age. % 59 Ho: Hours of sleep per night is independent of age. H₂: Hours of sleep per night is not independent of age. % % 75 Ho: 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.) 90 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? 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. 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. (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? Fewer than 6 6 to 6.9