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 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. Họ: Hours of sleep per night is not independent of age. H: Hours of sleep per night is independent of age. O Ho: 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 Ho: Hours of sleep per night is mutually exclusive from age. H: Hours of sleep per night is not mutually exclusive from age. O Ho: Hours of sleep per night is independent of age. H: Hours of sleep per night is not 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 = Using a 0.05 level of significance, what is your conclusion? O Reject Ho. We conclude that hours of sleep per night and age are not independent. O Do not reject Ho. We cannot conclude that hours of sleep per night and age are not independent. O Reject Ho. We conclude that hours of sleep per night and age are independent. Do not reject Ho. We cannot conclude that hours of sleep per night and age are independent.
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 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. Họ: Hours of sleep per night is not independent of age. H: Hours of sleep per night is independent of age. O Ho: 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 Ho: Hours of sleep per night is mutually exclusive from age. H: Hours of sleep per night is not mutually exclusive from age. O Ho: Hours of sleep per night is independent of age. H: Hours of sleep per night is not 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 = Using a 0.05 level of significance, what is your conclusion? O Reject Ho. We conclude that hours of sleep per night and age are not independent. O Do not reject Ho. We cannot conclude that hours of sleep per night and age are not independent. O Reject Ho. We conclude that hours of sleep per night and age are independent. Do not reject Ho. We cannot conclude that hours of sleep per night and age are independent.
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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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
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.
Ho: Hours of sleep per night is not independent of age.
: Hours of sleep per night is independent of age.
Ha
Ho:
: 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.
Ho: Hours of sleep per night is mutually exclusive from age.
H: Hours of sleep per night is not mutually exclusive from age.
Ho: Hours of sleep per night is independent of age.
H: Hours of sleep per night is not 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
Using a 0.05 level of significance, what is your conclusion?
Reject Ho. We conclude that hours of sleep per night and age are not independent.
Do not reject Ho: We cannot conclude that hours of sleep per night and age are not independent.
Reject Ho. We conclude that hours of sleep per night and age are independent.
Do not reject Ho: We cannot conclude that hours of sleep per night and age are independent.
.0
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
%
Expert Solution
Step 1
(a)
(i)
The hypothesis can be formed as
Therefore, (d) is the correct option.
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