You may need to use the appropriate technology to answer this 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 38 36 6 to 6.9 60 57 7 to 7.9 77 75 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. H0: Hours of sleep per night is mutually exclusive from age. Ha: Hours of sleep per night is not mutually exclusive from age.H0: Hours of sleep per night is independent of age. Ha: Hours of sleep per night is not 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. Ha: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups.H0: Hours of sleep per night is not independent of age. Ha: Hours of sleep per night is independent of age. 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 = 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 : %

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	60	57
7 to 7.9	77	75
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.

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

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 =

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 : %

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