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	Age Group
39 or younger	40 or older
Fewer than 6	38	36
6 to 6.9	62	59
7 to 7.9	77	75
8 or more	63	90

(a)Conduct a test of independence to determine whether hours of sleep are independent of age.

State the null and alternative hypotheses.

H₀: Hours of sleep per night is independent of age. H_a: Hours of sleep per night is not independent of age.

H₀: Hours of sleep per night is mutually exclusive from age. H_a: Hours of sleep per night is not mutually exclusive from age.

H₀: Hours of sleep per night is not independent of age. H_a: Hours of sleep per night is independent of age.

H₀: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups. H_a: 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?

Reject H₀. We conclude that hours of sleep per night and age are not independent.

Reject H₀. We cannot conclude that hours of sleep per night and age are not independent.

Do not reject H₀. We cannot conclude that hours of sleep per night and age are not independent.

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 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 %_______

7 to 7.9 %_______

8 or more %_______