Complete the table. Report all answers accurate to three decimal places. Category A B C D Observed Expected Frequency Frequency = 13 29 18 13 What is the chi-square test-statistic for this data? x² What is the P-Value? P-Value =
Complete the table. Report all answers accurate to three decimal places. Category A B C D Observed Expected Frequency Frequency = 13 29 18 13 What is the chi-square test-statistic for this data? x² What is the P-Value? P-Value =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Conducting a Multinomial Chi-Square Goodness of Fit Test
You are conducting a multinomial Chi-Square Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:
\[ H_o : p_A = 0.3; \, p_B = 0.4; \, p_C = 0.15; \, p_D = 0.15 \]
### Task
Complete the table. Report all answers accurate to three decimal places.
#### Frequency Table
| Category | Observed Frequency | Expected Frequency |
|----------|--------------------|--------------------|
| A | 13 | |
| B | 29 | |
| C | 18 | |
| D | 13 | |
### Questions
1. **What is the chi-square test-statistic for this data?**
\[ \chi^2 = \]
2. **What is the P-Value?**
\[ \text{P-Value} = \]
### Instructions
- Calculate the expected frequency for each category using the given proportions.
- Apply the chi-square formula to determine the test-statistic.
- Use the test-statistic to find the P-value corresponding to the chi-square distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faddcfefe-79de-4bfb-b00e-9692daf48932%2Fb0084d2d-3adc-4e5e-89d5-6ae317b09c05%2Fihe7t19_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Conducting a Multinomial Chi-Square Goodness of Fit Test
You are conducting a multinomial Chi-Square Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:
\[ H_o : p_A = 0.3; \, p_B = 0.4; \, p_C = 0.15; \, p_D = 0.15 \]
### Task
Complete the table. Report all answers accurate to three decimal places.
#### Frequency Table
| Category | Observed Frequency | Expected Frequency |
|----------|--------------------|--------------------|
| A | 13 | |
| B | 29 | |
| C | 18 | |
| D | 13 | |
### Questions
1. **What is the chi-square test-statistic for this data?**
\[ \chi^2 = \]
2. **What is the P-Value?**
\[ \text{P-Value} = \]
### Instructions
- Calculate the expected frequency for each category using the given proportions.
- Apply the chi-square formula to determine the test-statistic.
- Use the test-statistic to find the P-value corresponding to the chi-square distribution.
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