(a) The results of this ANOVA test are summarized in the ANOVA table below. Complete the missing cell in the ANOVA table (round your answer to at least two decimal places). Source of Degrees of Sum of Mean square F statistic ? variation freedom squares Treatments (between 3 369.05 123.02 groups) Error (within 934 98,097.6 105.03 groups) Total 937 98,466.65 (b) How many countries total were studied? (c) For the ANOVA test, it is assumed that the population variances of flight delay times are equal for each country studied. What is an unbiased estimate of this common population variance based on the sample variances? (d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.
(a) The results of this ANOVA test are summarized in the ANOVA table below. Complete the missing cell in the ANOVA table (round your answer to at least two decimal places). Source of Degrees of Sum of Mean square F statistic ? variation freedom squares Treatments (between 3 369.05 123.02 groups) Error (within 934 98,097.6 105.03 groups) Total 937 98,466.65 (b) How many countries total were studied? (c) For the ANOVA test, it is assumed that the population variances of flight delay times are equal for each country studied. What is an unbiased estimate of this common population variance based on the sample variances? (d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places.
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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![### Exploring Air Traffic Control: An ANOVA Analysis
#### Context:
In the United States, the air traffic control system is under government control. However, there is debate about whether privatization would be beneficial, particularly concerning the frequency of flight delays.
#### Hypothesis:
To determine if U.S. flight delays are significantly different compared to other countries, a one-way, independent-samples ANOVA test is conducted. This test examines if there are differences in average flight delay times among several countries.
#### Data Analysis:
##### ANOVA Table:
- **Source of Variation:** Effects split into parts to isolate factors contributing to variation.
- **Degrees of Freedom (df):** Shows the number of independent values able to vary in analysis.
- **Sum of Squares (SS):** Measures total variation within data.
- **Mean Square (MS):** Average variation per degree of freedom.
- **F statistic:** Ratio used to determine significance.
| Source of Variation | Degrees of Freedom | Sum of Squares | Mean Square | F statistic |
|---------------------|--------------------|----------------|-------------|-------------|
| Treatments (between groups) | 3 | 369.05 | 123.02 | [ ] |
| Error (within groups) | 934 | 98,097.6 | 105.03 | |
| Total | 937 | 98,466.65 | | |
##### Analysis Questions:
(a) **Filling the ANOVA Table:** Calculate the missing F statistic (round to at least two decimal places).
(b) **Countries Studied:** Determine number of countries based on degrees of freedom.
[ ]
(c) **Estimate Variance:** Assume equal population variances for delay times; estimate common population variance.
[ ]
(d) **p-value:** Find the p-value for the calculated F statistic, rounding to three decimal places.
[ ]
(e) **Conclusion Using 0.01 Significance Level:** Decide if differences exist in mean delay times among countries.
- Yes ☐ No ☐
##### Diagram/Graph Explanation:
The document includes an ANOVA table displaying elements to compare flight delay variances across different countries. This statistical method helps discern if observed variances are larger than expected by chance, guiding decisions on the hypothesis.
Examining this data allows for informed decisions on whether privatization of air traffic control could alleviate delay issues in the U.S. This educational tool provides practical insight into the use](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F438f9e3e-5163-4042-928f-6af00166f2ed%2Fcfeaabfb-5807-49d7-922b-92ece3c2515d%2Fkk0uw8_processed.png&w=3840&q=75)
Transcribed Image Text:### Exploring Air Traffic Control: An ANOVA Analysis
#### Context:
In the United States, the air traffic control system is under government control. However, there is debate about whether privatization would be beneficial, particularly concerning the frequency of flight delays.
#### Hypothesis:
To determine if U.S. flight delays are significantly different compared to other countries, a one-way, independent-samples ANOVA test is conducted. This test examines if there are differences in average flight delay times among several countries.
#### Data Analysis:
##### ANOVA Table:
- **Source of Variation:** Effects split into parts to isolate factors contributing to variation.
- **Degrees of Freedom (df):** Shows the number of independent values able to vary in analysis.
- **Sum of Squares (SS):** Measures total variation within data.
- **Mean Square (MS):** Average variation per degree of freedom.
- **F statistic:** Ratio used to determine significance.
| Source of Variation | Degrees of Freedom | Sum of Squares | Mean Square | F statistic |
|---------------------|--------------------|----------------|-------------|-------------|
| Treatments (between groups) | 3 | 369.05 | 123.02 | [ ] |
| Error (within groups) | 934 | 98,097.6 | 105.03 | |
| Total | 937 | 98,466.65 | | |
##### Analysis Questions:
(a) **Filling the ANOVA Table:** Calculate the missing F statistic (round to at least two decimal places).
(b) **Countries Studied:** Determine number of countries based on degrees of freedom.
[ ]
(c) **Estimate Variance:** Assume equal population variances for delay times; estimate common population variance.
[ ]
(d) **p-value:** Find the p-value for the calculated F statistic, rounding to three decimal places.
[ ]
(e) **Conclusion Using 0.01 Significance Level:** Decide if differences exist in mean delay times among countries.
- Yes ☐ No ☐
##### Diagram/Graph Explanation:
The document includes an ANOVA table displaying elements to compare flight delay variances across different countries. This statistical method helps discern if observed variances are larger than expected by chance, guiding decisions on the hypothesis.
Examining this data allows for informed decisions on whether privatization of air traffic control could alleviate delay issues in the U.S. This educational tool provides practical insight into the use
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