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

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(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
Transcribed Image Text:(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
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.
Age Group
Hours of Sleep
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.
O H: Hours of sleep per night is mutually exclusive from age.
: Hours of sleep per night is not mutually exclusive from age.
O H: Hours of sleep per night is independent of age.
H: Hours of sleep per night is not independent of age.
O H: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups.
H: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups.
O H: Hours of sleep per night is not independent of age.
H: 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
%3D
Using a 0.05 level of significance, what is your conclusion?
O Do not reject H. We cannot conclude that hours of sleep per night and age are not independent.
O Reject H- We cannot conclude that hours of sleep per night and age are not independent.
O Do not reject H. We conclude that hours of sleep per night and age are not independent.
O Reject H. We conclude that hours of sleep per night and age are not independent.
1:24 PM
Transcribed Image Text: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. Age Group Hours of Sleep 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. O H: Hours of sleep per night is mutually exclusive from age. : Hours of sleep per night is not mutually exclusive from age. O H: Hours of sleep per night is independent of age. H: Hours of sleep per night is not independent of age. O H: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups. H: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups. O H: Hours of sleep per night is not independent of age. H: 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 %3D Using a 0.05 level of significance, what is your conclusion? O Do not reject H. We cannot conclude that hours of sleep per night and age are not independent. O Reject H- We cannot conclude that hours of sleep per night and age are not independent. O Do not reject H. We conclude that hours of sleep per night and age are not independent. O Reject H. We conclude that hours of sleep per night and age are not independent. 1:24 PM
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