a. Formulate a hypotheses that can be used to test for equal proportions of respondents who say they are willing (or not willing) to repurchase their current vehicle. 1. Ho : P1 * P2 * p3 2. Ho : P1 = P2 = P3 3. Ho : P1 * P2 = P3 Choose the correct answer from the list above. 2 0 Choose the correct alternative hypothesis: All population proportions are not equal b. Enter the values from the expected frequency table (to 2 decimals if necessary). Chevrolet Impala Ford Fusion Honda Accord Total Yes No Total c. What is the value of the test statistic (to 2 decimals)? d. What is the p-value (to 4 decimals)? e. What is your conclusion at a = 0.05? Conclude that the three makes of automobiles provide equal proportions of consumer loyalty
a. Formulate a hypotheses that can be used to test for equal proportions of respondents who say they are willing (or not willing) to repurchase their current vehicle. 1. Ho : P1 * P2 * p3 2. Ho : P1 = P2 = P3 3. Ho : P1 * P2 = P3 Choose the correct answer from the list above. 2 0 Choose the correct alternative hypothesis: All population proportions are not equal b. Enter the values from the expected frequency table (to 2 decimals if necessary). Chevrolet Impala Ford Fusion Honda Accord Total Yes No Total c. What is the value of the test statistic (to 2 decimals)? d. What is the p-value (to 4 decimals)? e. What is your conclusion at a = 0.05? Conclude that the three makes of automobiles provide equal proportions of consumer loyalty
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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![### Hypothesis Testing for Equal Proportions
#### a. Formulating Hypotheses
To test for equal proportions of respondents who say they are willing (or not willing) to repurchase their current vehicle, we set up the following hypotheses:
1. \( H_0 : p_1 \neq p_2 \neq p_3 \)
2. \( H_0 : p_1 = p_2 = p_3 \)
3. \( H_0 : p_1 \neq p_2 = p_3 \)
**Correct Answer:** Option 2
**Alternative Hypothesis:** All population proportions are not equal.
#### b. Expected Frequency Table
Enter the values from the expected frequency table (to 2 decimals if necessary):
| | Chevrolet Impala | Ford Fusion | Honda Accord | Total |
|---------------------|------------------|-------------|--------------|-------|
| Yes | | | | |
| No | | | | |
| Total | | | | |
#### c. Test Statistic Value
What is the value of the test statistic (to 2 decimals)?
\[ \boxed{} \]
#### d. p-value Calculation
What is the p-value (to 4 decimals)?
\[ \boxed{} \]
#### e. Conclusion at \( \alpha = 0.05 \)
**Conclusion:** Conclude that the three makes of automobiles provide equal proportions of consumer loyalty.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a11e060-92c7-4c99-b32c-8bbf9de3d4ca%2F257c3814-4082-4be3-8d19-6dfbadcfa173%2Fl5efohp_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Equal Proportions
#### a. Formulating Hypotheses
To test for equal proportions of respondents who say they are willing (or not willing) to repurchase their current vehicle, we set up the following hypotheses:
1. \( H_0 : p_1 \neq p_2 \neq p_3 \)
2. \( H_0 : p_1 = p_2 = p_3 \)
3. \( H_0 : p_1 \neq p_2 = p_3 \)
**Correct Answer:** Option 2
**Alternative Hypothesis:** All population proportions are not equal.
#### b. Expected Frequency Table
Enter the values from the expected frequency table (to 2 decimals if necessary):
| | Chevrolet Impala | Ford Fusion | Honda Accord | Total |
|---------------------|------------------|-------------|--------------|-------|
| Yes | | | | |
| No | | | | |
| Total | | | | |
#### c. Test Statistic Value
What is the value of the test statistic (to 2 decimals)?
\[ \boxed{} \]
#### d. p-value Calculation
What is the p-value (to 4 decimals)?
\[ \boxed{} \]
#### e. Conclusion at \( \alpha = 0.05 \)
**Conclusion:** Conclude that the three makes of automobiles provide equal proportions of consumer loyalty.
Transcribed Image Text:### Excel Worksheet Summary
This Excel worksheet is set up to analyze car repurchase frequencies across three brands: Chevrolet, Ford, and Honda. It includes observed and expected repurchase data, chi-square computations, and a bar chart visualizing the data.
#### Observed Data
The observed frequencies for whether customers are likely to repurchase a vehicle from Chevrolet, Ford, or Honda are listed:
- **Chevrolet:**
- Yes: 72
- No: 53
- **Ford:**
- Yes: 121
- No: 79
- **Honda:**
- Yes: 123
- No: 52
#### Expected Data
The expected repurchase frequencies (not filled in in this sheet) should be calculated based on the hypothesis being tested.
#### Chi-Square Computation
The chi-square computation section outlines the process for testing the statistical significance of the difference between observed and expected frequencies. It includes columns for:
- **Observed Frequency**
- **Expected Frequency**
- **Difference**
- **Difference Squared**
- **Difference Squared / Expected**
The computed chi-square value and p-value will determine if the null hypothesis (that observed frequencies equal expected frequencies) can be rejected.
- **Alpha Level:** 0.025
The outcomes are summarized in the table at the right for Chevrolet, Ford, and Honda, indicating whether to reject the null hypothesis.
#### Bar Chart
The bar chart titled "Repurchase Frequencies (Observed vs. Expected)" provides a visual comparison of the observed frequencies. Only the observed values are evident; expected values need to be entered for comparison.
#### Additional Notes
- Cells marked with `#N/A` indicate missing computations that need to be entered for a complete analysis.
- The summary section states whether to reject the null hypothesis for each brand.
This setup can be used for educational purposes to illustrate how chi-square tests are applied in real-world situations, specifically in market analysis and consumer behavior studies.
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