Concept explainers
(a)
To compare: The scores of the Machine A and Machine B
(a)
Explanation of Solution
Given information:
The stem and leaf diagram for the two machines is given below
Machine A | Machine B | |
5 | 3, 5, 9 | |
6,1 | 4 | 2, 5, 7 |
9,7,4,1,1 | 3 | 2, 4, 8, 9 |
8,7,6,3,2,0 | 2 | 1, 5, 9 |
5,4 | 1 | 0 |
0 | 2 |
Formula used:
Calculation:
For machine A
Median
Skewness
Most of the data values are between
It seems to be symmetric roughly.
For machine B
Median
Skewness
Most of the data values are between
It seems to be negatively skewed as it is skewed towards left.
Conclusion:
Center
Center can be compared on the basis of median.
Here,
Spread
Here, machine B is more spread than machine A as the range of machine B is greater than machine A.
Skewness
Machine A is roughly symmetrical while Machine B is negatively skewed.
(b)
To find: The machine achieving the overall highest gain.
(b)
Answer to Problem 15PT1
Machine B should be advertised.
Explanation of Solution
Formula used:
Calculation:
The machine achieving overall highest gain can be decided on the basis of the average gain in cardiovascular fitness.
For machine A
For machine B
Conclusion:
Mean overall gain is higher in machine B.
(c)
To find: The machine with highest consistency.
(c)
Answer to Problem 15PT1
Machine A should be advertised for the most consistent gain in cardiovascular fitness.
Explanation of Solution
Formula used:
Calculation:
The consistency can be measured by variance.
More variance is an indication of less consistency.
For machine A
For machine B
Conclusion:
The variance of machine B is greater than machine A.
(d)
To find: The reason for limitedness of the experiment.
(d)
Explanation of Solution
Here, the volunteers are chosen from the area near the company’s headquarters.
This may not represent the entire population of the cardiovascular fitness gain. Other centres may vary in results.
Chapter 4 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Intro Stats, Books a la Carte Edition (5th Edition)
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Basic Business Statistics, Student Value Edition
Statistics for Psychology
Elementary Statistics: Picturing the World (7th Edition)
Introductory Statistics (10th Edition)
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