A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was

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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.
(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 not independent of age. Ha:
Hours of sleep per night is independent of age.
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.
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?
Do not reject H0. We cannot conclude that hours of sleep per
night and age are not independent.
Reject H0. We conclude that hours of sleep per night and age are
not independent.
Reject H0. We cannot conclude that hours of sleep per night and
age are not independent.
Do not reject H0. We conclude that hours of sleep per night and
age are not 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 %=