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In: Statistics and Probability

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

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 Sleep Age Group
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.

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 conclude that hours of sleep per night and age are 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 independent.Do not reject H0. We cannot 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 %

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orchestra answered 1 year ago
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