(a) Conduct a test of independence to determine whether hours of sleep are independent of age. State the null and alternative hypotheses. O Hg: 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. Ho: Hours of sleep per night is mutually exclusive from age. H: Hours of sleep per night is not mutually exclusive from age. Hoi 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 Hg. We conclude that hours of sleep per night and age are not independent. O Reject Hg. We conclude that hours of sleep per night and age are independent. O Do not reject Hg. We cannot conclude that hours of sleep per night and age are not independent. O Do not reject H.. We cannot conclude that hours of sleep per nioht and age are independent.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 13PT

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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.
Age Group
Hours of Sleep
39 or younger
40 or older
Fewer than 6
36
34
6 to 6.9
60
57
7 to 7.9
77
75
8 or more
67
94
(a) Conduct a test of independence to determine whether hours of sleep are independent of age.
State the null and alternative hypotheses.
O Ho: Hours of sleep per night is not independent of age.
H: Hours of sleep per night is 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 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 Reject H,. We conclude that hours of sleep per night and age are independent.
O Do not reject H. We cannot conclude that hours of sleep per night and age are not independent.
O Do not reject H,. We cannot conclude that hours of sleep per night and age are independent.

O Do not reject H.. We cannot 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
%

Expert Solution

Working

Observed	Expected	(O-E)^2	(O-E)^2/E
36	33.6	5.76	0.171429
60	56.16	14.7456	0.262564
77	72.96	16.3216	0.223706
67	77.28	105.6784	1.367474
34	36.4	5.76	0.158242
57	60.84	14.7456	0.242367
75	79.04	16.3216	0.206498
94	83.72	105.6784	1.262284

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