Question

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	40	38
6 to 6.9	60	57
7 to 7.9	75	73
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:

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

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

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

D. 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.)

Using a 0.05 level of significance, what is your conclusion?

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

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

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

D. Do not reject H₀. We conclude that hours of sleep per night and age are 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: _____%

Answer 1

Answer:

a)A)H0: Hours of sleep per night is independent of age.
Ha: Hours of sleep per night is not independent of age

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

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