You are conducting a multinomial hypothesis test (a = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table. Observed Expected Frequency Frequency Category A 6 12 с 12 D 20 E 17 Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.
You are conducting a multinomial hypothesis test (a = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table. Observed Expected Frequency Frequency Category A 6 12 с 12 D 20 E 17 Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.
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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![### Educational Resource: Conducting a Multinomial Hypothesis Test
#### Hypothesis Testing Scenario
You are conducting a multinomial hypothesis test (\(\alpha = 0.05\)) with the claim that all five categories are equally likely to be selected.
#### Data Table
The table below forms the basis of your hypothesis test:
| Category | Observed Frequency | Expected Frequency |
|----------|--------------------|--------------------|
| A | 6 | |
| B | 12 | |
| C | 12 | |
| D | 20 | |
| E | 17 | |
**Note:** Report all answers accurate to three decimal places, retaining unrounded numbers for future calculations.
#### Questions to Address
1. **Chi-square Test-statistic (\(\chi^2\))**
Calculate the chi-square test-statistic, ensuring accuracy to three decimal places. Use unrounded Pearson residuals in your calculations.
\(\chi^2 =\) [Provide answer box]
2. **Degrees of Freedom (d.f.)**
Determine the degrees of freedom for this test.
\(d.f. =\) [Provide answer box]
3. **P-value for the Sample**
Compute the p-value for this sample, providing the answer to four decimal places.
p-value = [Provide answer box]
4. **Comparison of P-value with \(\alpha\)**
Decide if the p-value is less than \(\alpha\):
- Yes
- No
This framework will guide you through the process of conducting and interpreting a multinomial hypothesis test with equal category likelihoods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab306750-7c99-4ab7-aa22-5313632298af%2Fbbf359c6-3211-44d6-82f7-cd85938e0e8e%2Fc15gr1n_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Resource: Conducting a Multinomial Hypothesis Test
#### Hypothesis Testing Scenario
You are conducting a multinomial hypothesis test (\(\alpha = 0.05\)) with the claim that all five categories are equally likely to be selected.
#### Data Table
The table below forms the basis of your hypothesis test:
| Category | Observed Frequency | Expected Frequency |
|----------|--------------------|--------------------|
| A | 6 | |
| B | 12 | |
| C | 12 | |
| D | 20 | |
| E | 17 | |
**Note:** Report all answers accurate to three decimal places, retaining unrounded numbers for future calculations.
#### Questions to Address
1. **Chi-square Test-statistic (\(\chi^2\))**
Calculate the chi-square test-statistic, ensuring accuracy to three decimal places. Use unrounded Pearson residuals in your calculations.
\(\chi^2 =\) [Provide answer box]
2. **Degrees of Freedom (d.f.)**
Determine the degrees of freedom for this test.
\(d.f. =\) [Provide answer box]
3. **P-value for the Sample**
Compute the p-value for this sample, providing the answer to four decimal places.
p-value = [Provide answer box]
4. **Comparison of P-value with \(\alpha\)**
Decide if the p-value is less than \(\alpha\):
- Yes
- No
This framework will guide you through the process of conducting and interpreting a multinomial hypothesis test with equal category likelihoods.
Transcribed Image Text:**Is the p-value less than α?**
- ○ yes
- ○ no
---
**This test statistic leads to a decision to…**
- ○ reject the null
- ○ accept the null
- ○ fail to reject the null
- ○ accept the alternative
---
**As such, the final conclusion is that…**
- ○ There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
- ○ There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
- ○ The sample data support the claim that all 5 categories are equally likely to be selected.
- ○ There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.
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