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...


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 SleepAge Group
39 or younger40 or older
Fewer than 63836
6 to 6.95855
7 to 7.97775
8 or more6794


(a)


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

State the null and alternative hypotheses.



H
0: Hours of sleep per night is independent of age.

H
a: Hours of sleep per night is not independent of age.



H
0: Hours of sleep per night is not independent of age.

H
a: Hours of sleep per night is independent of age.



H
0: Hours of sleep per night is mutually exclusive from age.

H
a: Hours of sleep per night is not mutually exclusive from age.



H
0: 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 thep-value? (Round your answer to four decimal places.)


p-value =


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


RejectH
0. We cannot conclude that hours of sleep per night and age are not independent.

Do not rejectH
0. We conclude that hours of sleep per night and age are not independent.

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

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







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 (       )%


Jun 07, 2022
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