Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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