Answered: c. The test-statistic for this data =…

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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$### Hypothesis Testing on Car Brand Preferences **Problem Statement:** Is there a difference in the car brand's countries for Midwesterners and people from the West Coast? Out of the 175 randomly selected Midwesterners surveyed, 68 had an American car, 82 had a car from Asia, and 25 had a car from another country. Of the 166 randomly selected people from the West Coast who were surveyed, 41 had an American car, 87 had a car from Asia, and 38 had a car from outside of the US and Asia. Conduct the appropriate hypothesis test using an α = 0.05 level of significance. #### Questions and Solutions: **a. What is the correct statistical test to use?** - **Answer:** - Homogeneity ✓ - Paired t-test - Independence - Goodness-of-Fit **b. What are the null and alternative hypotheses?** - **$H_0$:** - Address and car brand's countries are dependent. - The distribution of car brand's countries is the same for Midwesterners and people from the west coast. ✓ - Address and car brand's countries are independent. - The distribution of car brand's countries is not the same for Midwesterners and people from the west coast. - **$H_1$:** - Address and car brand's countries are independent. - Address and car brand's countries are dependent. - The distribution of car brand's countries is not the same for Midwesterners and people from the west coast. ✓ - The distribution of car brand's countries is the same for Midwesterners and people from the west coast. **c. The test-statistic for this data = _____ (Please show your answer to three decimal places.)** **d. The p-value for this sample = _____ (Please show your answer to four decimal places.)** **e. The p-value is less than (or equal to) α** **f. Based on this, we should** - reject the null - fail to reject the null ### Explanation of Selection: 1. **Statistical Test Selection**: - Homogeneity test is appropriate because we are comparing the distribution of a categorical variable (car brand's country) across different populations (Midwesterners and people from the West Coast). 2. **Hypotheses**:$

Transcribed Image Text:### Hypothesis Testing on Car Brand Preferences **Problem Statement:** Is there a difference in the car brand's countries for Midwesterners and people from the West Coast? Out of the 175 randomly selected Midwesterners surveyed, 68 had an American car, 82 had a car from Asia, and 25 had a car from another country. Of the 166 randomly selected people from the West Coast who were surveyed, 41 had an American car, 87 had a car from Asia, and 38 had a car from outside of the US and Asia. Conduct the appropriate hypothesis test using an α = 0.05 level of significance. #### Questions and Solutions: **a. What is the correct statistical test to use?** - **Answer:** - Homogeneity ✓ - Paired t-test - Independence - Goodness-of-Fit **b. What are the null and alternative hypotheses?** - **$H_0$:** - Address and car brand's countries are dependent. - The distribution of car brand's countries is the same for Midwesterners and people from the west coast. ✓ - Address and car brand's countries are independent. - The distribution of car brand's countries is not the same for Midwesterners and people from the west coast. - **$H_1$:** - Address and car brand's countries are independent. - Address and car brand's countries are dependent. - The distribution of car brand's countries is not the same for Midwesterners and people from the west coast. ✓ - The distribution of car brand's countries is the same for Midwesterners and people from the west coast. **c. The test-statistic for this data = _____ (Please show your answer to three decimal places.)** **d. The p-value for this sample = _____ (Please show your answer to four decimal places.)** **e. The p-value is less than (or equal to) α** **f. Based on this, we should** - reject the null - fail to reject the null ### Explanation of Selection: 1. **Statistical Test Selection**: - Homogeneity test is appropriate because we are comparing the distribution of a categorical variable (car brand's country) across different populations (Midwesterners and people from the West Coast). 2. **Hypotheses**:

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