Researchers measured the waist sizes of 230 men in a study on body fat. The true mean and standard deviation of the waist sizes for the 230 men are 36.417 inches and 4.081 inches, respectively. To explore variation of the mean from sample to sample, they simulated by drawing many samples of size 2, 5, 10, and 20 with replacement, from the 230 measurer accompanying table. Complete parts a through d below. Histograms and summary statistics Click the icon to view the histograms and summary statistics. a) According to the Central Limit Theorem, what should the theoretical mean and standard deviation be for each of these sample sizes? st. dev. Mean 2 JUL 5 10 (Round to three decimal places as needed.) n 20 of Subjects 400- 0- 26 Samples of Size 10 2000 1500- 1000- 500- 0- Waist Size (inches) 32 50 n 2 5 10 20 40 Waist Size (inches) G Q 2 # of Subjects Mean 36.378 36.444 36.406 36.412 1000 500- 0- 30 Samples of Size 20 2500 2000- 1500- 1000- 500- 44 Waist Size (inches) 04- 33 Waist Size (inches) st. dev. D 2.899 1.788 1.318 0.906 40 G Q Q
Researchers measured the waist sizes of 230 men in a study on body fat. The true mean and standard deviation of the waist sizes for the 230 men are 36.417 inches and 4.081 inches, respectively. To explore variation of the mean from sample to sample, they simulated by drawing many samples of size 2, 5, 10, and 20 with replacement, from the 230 measurer accompanying table. Complete parts a through d below. Histograms and summary statistics Click the icon to view the histograms and summary statistics. a) According to the Central Limit Theorem, what should the theoretical mean and standard deviation be for each of these sample sizes? st. dev. Mean 2 JUL 5 10 (Round to three decimal places as needed.) n 20 of Subjects 400- 0- 26 Samples of Size 10 2000 1500- 1000- 500- 0- Waist Size (inches) 32 50 n 2 5 10 20 40 Waist Size (inches) G Q 2 # of Subjects Mean 36.378 36.444 36.406 36.412 1000 500- 0- 30 Samples of Size 20 2500 2000- 1500- 1000- 500- 44 Waist Size (inches) 04- 33 Waist Size (inches) st. dev. D 2.899 1.788 1.318 0.906 40 G Q Q
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
Transcribed Image Text:Researchers measured the waist sizes of 230 men in a study on body fat. The true mean and standard deviation of the waist sizes for the 230 men are 36.417 inches and 4.081 inches, respectively. To explore variation of the
mean from sample to sample, they simulated by drawing many samples of size 2, 5, 10, and 20 with replacement, from the 230 measurer
accompanying table. Complete parts a through d below.
Histograms and summary statistics
Click the icon to view the histograms and summary statistics.
a) According to the Central Limit Theorem, what should the theoretical mean and standard deviation be for each of these sample sizes?
st. dev.
n
2
Mean
C...
5
10
20
(Round to three decimal places as needed.)
S 0007
5
400-
*
# of Subjects
0+
26
38
Waist Size (inches)
Samples of Size 10
2000-
1500-
1000-
500-
0
32
n
2
Waist Size (inches)
512
50
10
20
40
Q
Q
G
# of Si
# of Subjects
Mean
36.378
36.444
36.406
36.412
1000-
500-
0+
30
Samples of Size 20
2500
2000-
1500-
1000-
500-
Waist Size (inches)
44
0+
33
Waist Size (inches)
st. dev.
2.899
1.788
1.318
0.906
40
Q
Q
Transcribed Image Text:Researchers measured the waist sizes of 230 men in a study on body fat. The true mean and standard deviation of the waist sizes for the 230 men are 36.417 inches and 4.081 inches, respectively. To explore variation of the
mean from sample to sample, they simulated by drawing many samples of size 2, 5, 10, and 20 with replacement, from the 230 measurements. The histograms and summary statistics for each simulation are shown in the
accompanying table. Complete parts a through d below.
Click the icon to view the histograms and summary statistics.
a) According to the Central Limit Theorem, what should the theoretical mean and standard deviation be for each of these sample sizes?
st. dev.
Mean
...
n
2
5
10
20
(Round to three decimal places as needed.)
Histograms and summary statistics
CO
5
*
# of Subjects
*
000
400-
0+
26
38
Waist Size (inches)
Samples of Size 10
2000-
1500-
1000-
500-
0
32
n
Waist Size (inches)
2690
5
50
10
40
Q
Q
5
*
# of Subjects
Mean
36.378
36.444
36.406
36.412
1000-
500-
0-
30
Waist Size (inches)
Samples of Size 20
2500
2000-
1500-
1000-
500-
0+
33
44
st. dev.
2.899
1.788
1.318
0.906
40
Waist Size (inches)
D
G
Q
G
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 15 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
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
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
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…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman