research scenario: a city planner is assessin...

research scenario: a city planner is assessing the distribution of how teenagers get to school to inform infrastructure improvements. the following observed frequencies for each mode of transportation were charted out of 300 teenagers surveyed.\nmodes of transportation to school\ntransportation observed frequency\nbus 75\ncar 60\nbike 65\nwalk 55\nskateboard 45\ntotal 300\nwrite the null and alternative hypotheses.\nnull hypothesis \nalternative hypothesis \nuse the table below to help you calculate the final chi - square statistic in the bottom right of the table.\ncategories observed frequency expected frequency o - e (o - e)^2 (o - e)^2/e\nbus 75 60 15 225 3.75\ncar 60 60 0 0 0\nbike 65 60 5 25 0.4167\nwalk 55 60 - 5 25 0.4167\nskateboard 45 60 - 15 225 3.75\ntotals 300 300 \ntotal chi - square value from table above 8.3333\np - value associated with this chi - square value 0.0801 (use your online calculator to verify the total chi - square value you calculated and to determine its associated p - value)\nconclusion

Answer

# Explanation: ## Step1: Define null hypothesis The null hypothesis ($H_0$) is that there is no difference in the distribution of the modes of transportation that teenagers use to get to school. In other words, the observed frequencies are equal to the expected frequencies. So, $H_0$: The distribution of modes of transportation to school is uniform. ## Step2: Define alternative hypothesis The alternative hypothesis ($H_1$) is that there is a difference in the distribution of the modes of transportation that teenagers use to get to school. So, $H_1$: The distribution of modes of transportation to school is not uniform. ## Step3: Interpret p - value The p - value associated with the chi - square value of 8.333 is 0.0801. If we assume a significance level ($\alpha$) of 0.05, since the p - value (0.0801) > $\alpha$ (0.05), we fail to reject the null hypothesis. # Answer: Null Hypothesis: The distribution of modes of transportation to school is uniform. Alternative Hypothesis: The distribution of modes of transportation to school is not uniform. Conclusion: Fail to reject the null hypothesis at the 0.05 significance level.