Concept explainers
Weight loss: A weight loss company claims that the median weight loss for people who follow their program is at least 15 pounds. Weight losses for a random sample of 20 people in the program were recorded, and the results were as follows. Can you conclude that the claim is false? Use the
- State the appropriate null and alternate hypotheses.
- Compute the value of the test statistic.
- Find the critical value.
- State a conclusion.
a.
To find:The value of test statistic.
Answer to Problem 11E
The hypothesis are
Explanation of Solution
Given information:
The given data is,
Concept used:
The test statistic is,
If the sample size is less than or equal to
If the sample size is greater than
Here, the number of times the less frequent sign occur is
The conditions for test statistics are shown below in table.
Type of test | Test statistic |
Right-tailed test | Number of minus signs |
Left-tailed test | Number of plus signs |
Two-tailed test | Number of plus or minus signs, whichever is smaller |
Calculations:
The hypothesis are,
Therefore, the hypothesis are
b.
To find:The value of test statistic.
Answer to Problem 11E
The value of test statistic is
Explanation of Solution
Given information:
The given data is,
Concept used:
The test statistic is,
If the sample size is less than or equal to
If the sample size is greater than
Here, the number of times the less frequent sign occur is
The conditions for test statistics are shown below in table.
Type of test | Test statistic |
Right-tailed test | Number of minus signs |
Left-tailed test | Number of plus signs |
Two-tailed test | Number of plus or minus signs, whichever is smaller |
Calculations:
The value of test statistic is shown below.
Sample | Difference | Signs |
14 | 14-15 =-I | - |
8 | 8-15 =-7 | - |
12 | 12 -15 =-3 | - |
17 | 17 -15=+2 | + |
15 | 15-15 =0 | 0 |
7 | 7-15= -8 | - |
7 | 7-15= -8 | - |
6 | 6-15 =-9 | - |
8 | 8-15 =-7 | - |
9 | 9-15 =--6 | - |
6 | 6-15=-9 | - |
11 | 11-15 =-4 | - |
2 | 2- 15=-13 | - |
0 | 0-15=-15 | - |
11 | 11-15 =-4 | - |
9 | 9-15 =--6 | - |
6 | 6-15 =-9 | - |
7 | 7-15= -8 | - |
6 | 6-15 =-9 | - |
17 | 17 - 15=+2 | + |
From the above table, the number of minus sign is
Since, the sample size is less than
The test statistic is given by the number of plus or minus sign which are smaller in number.
Therefore, the value of test statistic for the given sample is
c.
To find:The critical value.
Answer to Problem 11E
The critical value is
Explanation of Solution
Given information:
The level of significance is
Calculations:
The critical value for one-tailed test at of significance of
Therefore, the critical value is
d.
To find:The conclusion for the test.
Answer to Problem 11E
The median weight loss for people who follow their program is less than
Explanation of Solution
Given information:
The level of significance is
Calculations:
The critical value for one-tailed test at of significance of
Since, the test statistics is
Thus, the hypothesis
Therefore, the median weight loss for people who follow their program is less than
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Chapter 15 Solutions
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