Elementary Statistics (Text Only)
2nd Edition
ISBN: 9780077836351
Author: Author
Publisher: McGraw Hill
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Chapter 15.2, Problem 11E
a.
To determine
To find:The hypothesis for the test statistic.
a.
Expert Solution
Answer to Problem 11E
The hypothesis are
Explanation of Solution
Given information:
The level of significance is
| Compact | ||||
| 34.5 | 33.7 | 26.1 | 28.5 | 27.4 |
| 30.6 | 31.1 | 28.0 | 33.0 | 33.0 |
| 32.8 | 28.5 | 25.5 | 32.1 | 34.9 |
| Midsize | ||||
| 21.6 | 21.1 | 29. 1 | 24.8 | 28.5 |
| 28.1 | 21.9 | 22.5 | 20.5 | 26.1 |
Calculations:
The hypothesis are,
Therefore, the hypothesis are
b.
To determine
To find:The value of test statistic.
b.
Expert Solution
Answer to Problem 11E
The value of test statistic is
Explanation of Solution
Given information:
The level of significance is
| Compact | ||||
| 34.5 | 33.7 | 26.1 | 28.5 | 27.4 |
| 30.6 | 31.1 | 28.0 | 33.0 | 33.0 |
| 32.8 | 28.5 | 25.5 | 32.1 | 34.9 |
| Midsize | ||||
| 21.6 | 21.1 | 29. 1 | 24.8 | 28.5 |
| 28.1 | 21.9 | 22.5 | 20.5 | 26.1 |
Calculations:
The rank table is shown below.
| Gas mileages | Sample | Rank |
| 20.5 | Midsize | 1 |
| 21.1 | Midsize | 2 |
| 21.6 | Midsize | 3 |
| 21.9 | Midsize | 4 |
| 22.5 | Compact | 5 |
| 24.8 | Midsize | 6 |
| 25.5 | Compact | 7 |
| 26.1 | Midsize | 8.5 |
| 26.1 | Compact | 8.5 |
| 27.4 | Compact | 10 |
| 28 | Compact | 11 |
| 28.1 | Midsize | 12 |
| 28.5 | Midsize | 14 |
| 28.5 | Compact | 14 |
| 28.5 | Compact | 14 |
| 29.1 | Midsize | 16 |
| 30.6 | Compact | 17 |
| 31.1 | Compact | 18 |
| 32.1 | Compact | 19 |
| 32.8 | Compact | 20 |
| 33 | Compact | 21.5 |
| 33 | Compact | 21.5 |
| 33.7 | Compact | 23 |
| 34.5 | Compact | 24 |
| 34.9 | Compact | 25 |
The sum of rank of compact car is
The sum of smaller rank is
The value of
Substitute the values in above equation.
The value of
Substitute the values in above equation.
The z- value is,
Substitute the values in above equation.
Therefore, the value of test statistics is
c.
To determine
To find:The p-value.
c.
Expert Solution
Answer to Problem 11E
The p-valueis
Explanation of Solution
Given information:
The level of significance is
| Compact | ||||
| 34.5 | 33.7 | 26.1 | 28.5 | 27.4 |
| 30.6 | 31.1 | 28.0 | 33.0 | 33.0 |
| 32.8 | 28.5 | 25.5 | 32.1 | 34.9 |
| Midsize | ||||
| 21.6 | 21.1 | 29. 1 | 24.8 | 28.5 |
| 28.1 | 21.9 | 22.5 | 20.5 | 26.1 |
Calculations:
From the table of cumulative
Therefore, the p-value is
d.
To determine
To find:The conclusion for the test.
d.
Expert Solution
Answer to Problem 11E
The median mileage is less for compact car than for the midsize car.
Explanation of Solution
Given information:
The level of significance is
| Compact | ||||
| 34.5 | 33.7 | 26.1 | 28.5 | 27.4 |
| 30.6 | 31.1 | 28.0 | 33.0 | 33.0 |
| 32.8 | 28.5 | 25.5 | 32.1 | 34.9 |
| Midsize | ||||
| 21.6 | 21.1 | 29. 1 | 24.8 | 28.5 |
| 28.1 | 21.9 | 22.5 | 20.5 | 26.1 |
Calculations:
Since, the p-value is
Thus, the hypothesis
Therefore, the median mileage is less for compact car than for the midsize car.
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Chapter 15 Solutions
Elementary Statistics (Text Only)
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