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 37 35 6 to 6.9 60 57 7 to 7.9 78 76 8 or more 65 92 (a) Conduct a test of independence to determine whether hours of sleep are independent of age. (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?
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 37 35 6 to 6.9 60 57 7 to 7.9 78 76 8 or more 65 92 (a) Conduct a test of independence to determine whether hours of sleep are independent of age. (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?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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
37
35
6 to 6.9
60
57
7 to 7.9
78
76
8 or more
65
92
(a) Conduct a test of independence to determine whether hours of sleep are independent of age.
(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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ea199ac-d9f9-432f-8dc8-6b9e2b6778a5%2Fe2cba1fc-6ea2-4a70-ad5a-f3ce6155f227%2F22p7q3_processed.jpeg&w=3840&q=75)
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
37
35
6 to 6.9
60
57
7 to 7.9
78
76
8 or more
65
92
(a) Conduct a test of independence to determine whether hours of sleep are independent of age.
(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?
![Now that we have the observed and expected frequencies, the other components for the test statistic can be
found. The following table gives the given observed data and the calculated expected frequencies. The sum of
all the values in the final column will be the x test statistic.
Complete the table, rounding values in the final column to four decimal places and x" to three decimal places.
Squared
Difference
Divided by
Expected
Frequency
Squared
Difference
Observed
Expected
Frequency
Hours
Difference
Age
Group
Frequency
of
-e,
Sleep
z("a - ")
5.9536
39 or
2.442 =
5.9536
Fewer
37 - 34.56 =
37
34.56
34.56
than 6
younger
2.44
0.1723
Fewer
than 6
40 or
0.159
35
37.44
-2.44
5.9536
older
6 to
39 or
3.84
60
56.16
14.7456
0.2626
6.9
younger
6 to
6.9
40 or
57
60.84
-3.84
0.2424
older
7 to
39 or
78
73.92
4.08
16.6464
7.9
younger
7 to
40 or
older
76
80.08
-4.08
16.6464
7.9
8 or
39 or
|-10.38
65
75.36
107.3296
1.4242
mоre
younger
40 or
older
8 or
92
81.64
10.36
107.3296
more
(f, - e,
4.008](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ea199ac-d9f9-432f-8dc8-6b9e2b6778a5%2Fe2cba1fc-6ea2-4a70-ad5a-f3ce6155f227%2Fxgnbd1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Now that we have the observed and expected frequencies, the other components for the test statistic can be
found. The following table gives the given observed data and the calculated expected frequencies. The sum of
all the values in the final column will be the x test statistic.
Complete the table, rounding values in the final column to four decimal places and x" to three decimal places.
Squared
Difference
Divided by
Expected
Frequency
Squared
Difference
Observed
Expected
Frequency
Hours
Difference
Age
Group
Frequency
of
-e,
Sleep
z("a - ")
5.9536
39 or
2.442 =
5.9536
Fewer
37 - 34.56 =
37
34.56
34.56
than 6
younger
2.44
0.1723
Fewer
than 6
40 or
0.159
35
37.44
-2.44
5.9536
older
6 to
39 or
3.84
60
56.16
14.7456
0.2626
6.9
younger
6 to
6.9
40 or
57
60.84
-3.84
0.2424
older
7 to
39 or
78
73.92
4.08
16.6464
7.9
younger
7 to
40 or
older
76
80.08
-4.08
16.6464
7.9
8 or
39 or
|-10.38
65
75.36
107.3296
1.4242
mоre
younger
40 or
older
8 or
92
81.64
10.36
107.3296
more
(f, - e,
4.008
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1 Part a
The computation is done as follow:
Hours of sleep | Age group | Observed frequencies (Oij) | Expected frequencies (Eij) | Eij-Oij | ||
Fewer than 6 | 39 or younger | 37 | 34.56 | 2.44 | 5.9536 | 0.172269 |
6 to 6.9 | 39 or younger | 60 | 56.16 | 3.84 | 14.7456 | 0.262564 |
7 to 7.9 | 39 or younger | 78 | 73.92 | 4.08 | 16.6464 | 0.225195 |
8 or more | 39 or younger | 65 | 75.36 | -10.36 | 107.3296 | 1.424225 |
Fewer than 6 | 40 or older | 35 | 37.44 | -2.44 | 5.9536 | 0.159017 |
6 to 6.9 | 40 or older | 57 | 60.84 | -3.84 | 14.7456 | 0.242367 |
7 to 7.9 | 40 or older | 76 | 80.08 | -4.08 | 16.6464 | 0.207872 |
8 or more | 40 or older | 92 | 81.64 | 10.36 | 107.3296 | 1.314669 |
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman