You mayr need to use the appropriate technology to answer this question. A surveyr 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 4D or older Fewer than 6 LC- 38 6 to 6.9 62- 57 7 to 7.9 T? 75 8 or more 63 :rH {a} Conduct a test of independence to determine whether hours of sleep are independent of age. State the null and alternative hypotheses. 'I_I' H0: Hours of sleep per night is not independent of age. Ha: Hours of sleep per night is independent of age. '3'} HD: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups. H6: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups. '3.:.3' H0: Hours of sleep per night is independent of age. Ha: Hours of sleep per night is not independent of age. HI]: Hours of sleep per night is mutuallyr exclusive from age. Ha: Hours of sleep per night is not mutually exclusive from age. Find the value of the test statistic. [Round your answer to three decimal places.} : What is the pvalue? (Round your answer to four decimal places.) Using a 0.05 level of signicance, what is your conclusion? '32:} Reject HO. We cannot conclude that hours of sleep per night and age are not independent. {:2- Reject Ho. We conclude that hours of sleep per night and age are not independent. {:1- Do not reject HQ. We cannot conclude that hours of sleep per night and age are not independent. '32:} Do not reject H0. 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 I5 hoursr 6 to 6.9 hours, 7" to 19 hours, and 8 hours or more per night? Fewer than 6 : \"fa 6 to 6.9 S % 7' to 19 E % 8 or more E %