Does mode of transportation depend on political party? Researchers asked a group of people about how they get to work. They also grouped the people by their political party. The data are recorded in the contingency table below, and the first few steps of a chi-square test of independence are summarized. (The observed values are above the expected values.) | | Car | Public Transit | Walk | Row Total | | :---------- | :-- | :------------- | :--- | :-------- | | Democrats | 5 | 12.8 | 17 | 22 | | Republicans | 23 | 21 | 8 | 44 | | Column Total| 28 | 33.8 | 25 | 66 | - $H_0$ : Political party does not affect mode of transportation (they are independent). - $H_a$ : Political party affects mode of transportation (they are dependent). - $\alpha=0.01$ - The test statistic, $\chi_0^2=17.900$. - Critical value: $\chi_{0.01}^2=9.210$.
Answer (2)
We reject the null hypothesis because the test statistic (17.900) is greater than the critical value (9.210). This indicates a significant relationship between mode of transportation and political party. Thus, mode of transportation depends on the political party.
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True
Explanation
Understand the problem and provided data We are given the test statistic χ 0 2 = 17.900 and the critical value χ 0.01 2 = 9.210 . We need to determine if the mode of transportation depends on political party.
Decision rule To determine whether to reject the null hypothesis, we compare the test statistic to the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Compare test statistic and critical value In this case, the test statistic χ 0 2 = 17.900 is greater than the critical value χ 0.01 2 = 9.210 . Therefore, we reject the null hypothesis.
Conclusion Since we reject the null hypothesis, we conclude that there is a statistically significant relationship between political party and mode of transportation. In other words, mode of transportation depends on political party.
Examples
Understanding the relationship between political affiliation and transportation choices can help urban planners and policymakers tailor transportation infrastructure and incentives to better serve different communities. For example, if one political group heavily relies on public transit, city planners can focus on improving public transit routes and services in areas where that group resides. Similarly, understanding the transportation needs of different political groups can inform the development of targeted policies and campaigns to promote sustainable transportation options.
