Listed below, from left to right and then top to bottom, are numbers of law enforcement fatalities for recent and consecutive years. First find the median, identify each value as being above the median or below the median, then test for randomness above and below the median using the runs test with a significance level of a = 0.05. Is there a trend? 176 197 172 154 168 160 185 184 155 157 181 145 167 246 164 138 182 181 148 208 Click the icon to view the critical values for number of runs G table.
Listed below, from left to right and then top to bottom, are numbers of law enforcement fatalities for recent and consecutive years. First find the median, identify each value as being above the median or below the median, then test for randomness above and below the median using the runs test with a significance level of a = 0.05. Is there a trend? 176 197 172 154 168 160 185 184 155 157 181 145 167 246 164 138 182 181 148 208 Click the icon to view the critical values for number of runs G table.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Critical Values for Runs Test for Randomness**
**Runs Test for Randomness: Critical Values for Number of Runs G**
This table displays the critical values for the number of runs (G) used in the Runs Test for Randomness, applicable for a two-tailed test with a significance level (α) of 0.05.
**Instructions:**
1. The table provides critical G values necessary for determining randomness in a dataset.
2. To use the table, find the intersection of `n1` (number of values below the median) and `n2` (number of values above the median).
**Conditions for Rejecting the Null Hypothesis of Randomness:**
- The null hypothesis can be rejected if either:
1. The number of runs G is less than or equal to the smaller entry in the table.
2. The number of runs G is greater than or equal to the larger entry in the table.
**Table:**
- Rows represent different values of `n1` ranging from 2 to 20.
- Columns represent different values of `n2` ranging from 2 to 20.
- The intersections provide the critical values of G needed for hypothesis testing.
**Example Usage:**
- If `n1` = 5 and `n2` = 6, locate the 5th row and the 6th column intersection for the critical value of G.
To apply the Runs Test for Randomness:
1. Determine the median of your dataset.
2. Count how many values are above (`n2`) and below (`n1`) the median.
3. Use the table to find the critical values of G for your `n1` and `n2`.
4. Compare your number of runs to the critical values to decide if randomness can be rejected.
**Note:**
This test helps in deciding whether an observed series deviates from randomness, which can indicate underlying patterns or influences on the dataset.
![### Analysis of Law Enforcement Fatalities Data
Below is a dataset representing the number of law enforcement fatalities over recent consecutive years. The numbers are arranged from left to right and then top to bottom:
- 176, 197, 172, 154, 168, 160
- 185, 184, 155, 157
- 181, 145, 167, 246, 164, 138
- 182, 181, 148, 208
---
#### Statistical Analysis
**1. Determine the Median:**
The dataset requires calculation of the median as an integer or a decimal.
**Input Box for the Median:**
- [ ]
**2. Hypothesis Testing:**
- Null Hypothesis (H₀):
- Alternative Hypothesis (H₁):
**Dropdown Boxes:**
- H₀: [ ]
- H₁: [ ]
**3. Calculate the Test Statistic:**
Determine the test statistic using the runs test for randomness above and below the median.
**Input Box for Test Statistic:**
- [ ]
**4. Critical Values:**
Identify the smaller and larger critical values from the table of critical values for the number of runs.
**Input Boxes for Critical Values:**
- Smaller critical value: [ ]
- Larger critical value: [ ]
**5. Conclusion of the Test:**
Draw conclusions based on the test statistic and critical values.
**Dropdown Box for Conclusion:**
- [ ]
### Trend Analysis
Evaluate whether there appears to be a trend in the number of law enforcement fatalities over the years.
**Dropdown Box for Trend:**
- There appears to be [ ] trend in the number of law enforcement fatalities because [ ].
This educational exercise guides the user through statistical analysis techniques, focusing on calculating medians, testing hypotheses, and interpreting trends.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff4f609e-581a-443b-8b38-f9a882250427%2F6499a6fc-fa5b-49a4-ba68-7f6984ba14a6%2F8ouy1jp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analysis of Law Enforcement Fatalities Data
Below is a dataset representing the number of law enforcement fatalities over recent consecutive years. The numbers are arranged from left to right and then top to bottom:
- 176, 197, 172, 154, 168, 160
- 185, 184, 155, 157
- 181, 145, 167, 246, 164, 138
- 182, 181, 148, 208
---
#### Statistical Analysis
**1. Determine the Median:**
The dataset requires calculation of the median as an integer or a decimal.
**Input Box for the Median:**
- [ ]
**2. Hypothesis Testing:**
- Null Hypothesis (H₀):
- Alternative Hypothesis (H₁):
**Dropdown Boxes:**
- H₀: [ ]
- H₁: [ ]
**3. Calculate the Test Statistic:**
Determine the test statistic using the runs test for randomness above and below the median.
**Input Box for Test Statistic:**
- [ ]
**4. Critical Values:**
Identify the smaller and larger critical values from the table of critical values for the number of runs.
**Input Boxes for Critical Values:**
- Smaller critical value: [ ]
- Larger critical value: [ ]
**5. Conclusion of the Test:**
Draw conclusions based on the test statistic and critical values.
**Dropdown Box for Conclusion:**
- [ ]
### Trend Analysis
Evaluate whether there appears to be a trend in the number of law enforcement fatalities over the years.
**Dropdown Box for Trend:**
- There appears to be [ ] trend in the number of law enforcement fatalities because [ ].
This educational exercise guides the user through statistical analysis techniques, focusing on calculating medians, testing hypotheses, and interpreting trends.
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