Q8 ### Chi-Square Test for Goodness of Fit**Objective:** Test for the claim that the following categories occur with the specified frequencies at the 0.05 significance level.- $ p_A = 0.3 $- $ p_B = 0.15 $- $ p_C = 0.15 $- $ p_D = 0.4 $Complete the table and the subsequent calculations, rounding all answers to three decimal places.#### Step 1: Complete the Table| Category | Observed Frequency | Expected Frequency | Residual ||----------|--------------------|---------------------|----------|| A | 22 | | || B | 22 | | || C | 12 | | || D | 31 | | |#### Step 2: Formulate Hypotheses- **Null Hypothesis $ H_0 $:** $ p_A = 0.3; \, p_B = 0.15; \, p_C = 0.15; \, p_D = 0.4 $- **Alternative Hypothesis $ H_1 $:** At least one proportion is different.**Original Claim:**- Select an answer from a drop-down menu to specify which hypothesis is the original claim.#### Step 3: Determine Critical Value of $ \chi^2 $Along with the significance level and degrees of freedom, place the critical value $ \chi^2_{\alpha, df} $ below the graph. **Graph Description:**The graph illustrates a $ \chi^2 $-distribution with a right-skewed curve. On the x-axis, the values range from 1 to 139, while the y-axis represents the probability, peaking early at around 20-30 on the x-axis.**Calculations:**- **Critical Value ( $ \chi^2_{\alpha, df} $):** Enter the value in the provided box.- **Degrees of Freedom ($ df $):** Number of categories - 1.#### Step 4: Compute Chi-Square Test Statistic- **Test Statistic:** Calculate and enter values rounded to three decimal places in the given box.- **p-value:** Determine the p-value and round it to four decimal places.#### Step 5: Make a Decision & Form Conclusion

Name: Q8 ### Chi-Square Test for Goodness of Fit**Objective:** Test for the
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Description: Q8 ### Chi-Square Test for Goodness of Fit**Objective:** Test for the claim that the following categories occur with the specified frequencies at the 0.05 significance level.- $ p_A = 0.3 $- $ p_B = 0.15 $- $ p_C = 0.15 $- $ p_D = 0.4 $Comple

Given : Category Observed frequency Expected Frequency Residual A 22 B 22 C 12…

Math

Statistics

Test for the claim that the following categories occur with the following frequencies: РА 3 0.3; рв %3D 0.15%;B рс —D 0.15;B pp %3D 0.4 Test at the 0.05 significance level. Complete the table. Round all answers to three decimal places. Observed Expected Frequency Frequency Category Residual A 22 В 22 12 D 31

Test for the claim that the following categories occur with the following frequencies: РА 3 0.3; рв %3D 0.15%;B рс —D 0.15;B pp %3D 0.4 Test at the 0.05 significance level. Complete the table. Round all answers to three decimal places. Observed Expected Frequency Frequency Category Residual A 22 В 22 12 D 31

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

### Chi-Square Test for Goodness of Fit

**Objective:** Test for the claim that the following categories occur with the specified frequencies at the 0.05 significance level.

- $ p_A = 0.3 $
- $ p_B = 0.15 $
- $ p_C = 0.15 $
- $ p_D = 0.4 $

Complete the table and the subsequent calculations, rounding all answers to three decimal places.

#### Step 1: Complete the Table

| Category | Observed Frequency | Expected Frequency | Residual |
|----------|--------------------|---------------------|----------|
| A | 22 | | |
| B | 22 | | |
| C | 12 | | |
| D | 31 | | |

#### Step 2: Formulate Hypotheses

- **Null Hypothesis $ H_0 $:** $ p_A = 0.3; \, p_B = 0.15; \, p_C = 0.15; \, p_D = 0.4 $
- **Alternative Hypothesis $ H_1 $:** At least one proportion is different.

**Original Claim:**
- Select an answer from a drop-down menu to specify which hypothesis is the original claim.

#### Step 3: Determine Critical Value of $ \chi^2 $

Along with the significance level and degrees of freedom, place the critical value $ \chi^2_{\alpha, df} $ below the graph.

**Graph Description:**
The graph illustrates a $ \chi^2 $-distribution with a right-skewed curve. On the x-axis, the values range from 1 to 139, while the y-axis represents the probability, peaking early at around 20-30 on the x-axis.

**Calculations:**
- **Critical Value ( $ \chi^2_{\alpha, df} $):** Enter the value in the provided box.
- **Degrees of Freedom ($ df $):** Number of categories - 1.

#### Step 4: Compute Chi-Square Test Statistic

- **Test Statistic:** Calculate and enter values rounded to three decimal places in the given box.
- **p-value:** Determine the p-value and round it to four decimal places.

#### Step 5: Make a Decision & Form Conclusion

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