MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.
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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.
### 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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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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