**Multinomial Hypothesis Test Example** You are conducting a multinomial hypothesis test (α = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table. | Category | Observed Frequency | Expected Frequency | |----------|--------------------|--------------------| | A | 8 | | | B | 23 | | | C | 12 | | | D | 20 | | | E | 23 | | ### (a) Determine the null and alternative hypotheses: 1. \( H_0: P_A = P_B = P_C = P_D = P_E = \frac{1}{5} \) - \( H_a: \) At least one proportion is different 2. \( H_0: P_A = P_B = P_C = P_D = P_E \) - \( H_a: \) At least one proportion is different 3. \( H_0: \) The categories are independent - \( H_a: \) The categories are dependent ### (b) What is the chi-square test statistic for this data? (Report answer accurate to three decimal places) \[ \chi^2 = \underline{\phantom{999}} \] ### (c) What are the degrees of freedom for this test? \[ \text{d.f.} = \underline{\phantom{9}} \] ### (d) What is the p-value for this sample? (Report answer accurate to four decimal places) \[ \text{p-value} = \underline{\phantom{9999}} \] ### (e) Is the p-value less than α? - [ ] yes - [ ] no **Instructions:** 1. Complete the table by calculating the expected frequencies. 2. Choose the appropriate null and alternative hypotheses. 3. Calculate and input the chi-square test statistic. 4. Determine the degrees of freedom and the p-value. 5. Conclude if the p-value is less than the significance level α.
**Multinomial Hypothesis Test Example** You are conducting a multinomial hypothesis test (α = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table. | Category | Observed Frequency | Expected Frequency | |----------|--------------------|--------------------| | A | 8 | | | B | 23 | | | C | 12 | | | D | 20 | | | E | 23 | | ### (a) Determine the null and alternative hypotheses: 1. \( H_0: P_A = P_B = P_C = P_D = P_E = \frac{1}{5} \) - \( H_a: \) At least one proportion is different 2. \( H_0: P_A = P_B = P_C = P_D = P_E \) - \( H_a: \) At least one proportion is different 3. \( H_0: \) The categories are independent - \( H_a: \) The categories are dependent ### (b) What is the chi-square test statistic for this data? (Report answer accurate to three decimal places) \[ \chi^2 = \underline{\phantom{999}} \] ### (c) What are the degrees of freedom for this test? \[ \text{d.f.} = \underline{\phantom{9}} \] ### (d) What is the p-value for this sample? (Report answer accurate to four decimal places) \[ \text{p-value} = \underline{\phantom{9999}} \] ### (e) Is the p-value less than α? - [ ] yes - [ ] no **Instructions:** 1. Complete the table by calculating the expected frequencies. 2. Choose the appropriate null and alternative hypotheses. 3. Calculate and input the chi-square test statistic. 4. Determine the degrees of freedom and the p-value. 5. Conclude if the p-value is less than the significance level α.
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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![**Multinomial Hypothesis Test Example**
You are conducting a multinomial hypothesis test (α = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.
| Category | Observed Frequency | Expected Frequency |
|----------|--------------------|--------------------|
| A | 8 | |
| B | 23 | |
| C | 12 | |
| D | 20 | |
| E | 23 | |
### (a) Determine the null and alternative hypotheses:
1. \( H_0: P_A = P_B = P_C = P_D = P_E = \frac{1}{5} \)
- \( H_a: \) At least one proportion is different
2. \( H_0: P_A = P_B = P_C = P_D = P_E \)
- \( H_a: \) At least one proportion is different
3. \( H_0: \) The categories are independent
- \( H_a: \) The categories are dependent
### (b) What is the chi-square test statistic for this data? (Report answer accurate to three decimal places)
\[ \chi^2 = \underline{\phantom{999}} \]
### (c) What are the degrees of freedom for this test?
\[ \text{d.f.} = \underline{\phantom{9}} \]
### (d) What is the p-value for this sample? (Report answer accurate to four decimal places)
\[ \text{p-value} = \underline{\phantom{9999}} \]
### (e) Is the p-value less than α?
- [ ] yes
- [ ] no
**Instructions:**
1. Complete the table by calculating the expected frequencies.
2. Choose the appropriate null and alternative hypotheses.
3. Calculate and input the chi-square test statistic.
4. Determine the degrees of freedom and the p-value.
5. Conclude if the p-value is less than the significance level α.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee710977-90c8-4f84-9cb1-1102aa3efb9b%2Fcd674252-9c1e-4967-b2ca-cd3fb831deb3%2Fl29e8p8.jpeg&w=3840&q=75)
Transcribed Image Text:**Multinomial Hypothesis Test Example**
You are conducting a multinomial hypothesis test (α = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.
| Category | Observed Frequency | Expected Frequency |
|----------|--------------------|--------------------|
| A | 8 | |
| B | 23 | |
| C | 12 | |
| D | 20 | |
| E | 23 | |
### (a) Determine the null and alternative hypotheses:
1. \( H_0: P_A = P_B = P_C = P_D = P_E = \frac{1}{5} \)
- \( H_a: \) At least one proportion is different
2. \( H_0: P_A = P_B = P_C = P_D = P_E \)
- \( H_a: \) At least one proportion is different
3. \( H_0: \) The categories are independent
- \( H_a: \) The categories are dependent
### (b) What is the chi-square test statistic for this data? (Report answer accurate to three decimal places)
\[ \chi^2 = \underline{\phantom{999}} \]
### (c) What are the degrees of freedom for this test?
\[ \text{d.f.} = \underline{\phantom{9}} \]
### (d) What is the p-value for this sample? (Report answer accurate to four decimal places)
\[ \text{p-value} = \underline{\phantom{9999}} \]
### (e) Is the p-value less than α?
- [ ] yes
- [ ] no
**Instructions:**
1. Complete the table by calculating the expected frequencies.
2. Choose the appropriate null and alternative hypotheses.
3. Calculate and input the chi-square test statistic.
4. Determine the degrees of freedom and the p-value.
5. Conclude if the p-value is less than the significance level α.
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