- Assume you are a researcher, please write null hypothesis and alternative hypothesis for the research question below (10’):
- Does the yearly income for Professors differ from Lawyers? Please write two-tailed hypothesis
- Is there a difference in memory retention between MPA students and MBA students? Please write two-tailed hypothesis
- Did dieters lose more fat than the exercisers? Please write two-tailed hypothesis
- Do people who take daily vitamins live longer than people who don’t? Please write one-tailed hypothesis
- Are engineers less extroverted compared to statisticians? Please write one-tailed hypothesis
- Assume you are a researcher, you want to examine whether cycling commuters are healthier than general population in the community. You are using BMI index as the measurement for health status. The average BMI index of general population in the community is 25, with population standard deviation, 1.5. You randomly selected 142 cycling commuters and collected their BMI index. The average BMI index of these 142 individuals is 23.5. With a 5% significance level, can you conclude that cycling commuters are healthier than general population in community? (2’)

*Cycling commuter:*

*Mean BMI: 23.5*

*N = 142*

*General population:*

*Mean BMI = 25*

*Standard deviation: 1.5*

- Please first write down two-tailed hypothesis (0.5’)
- Given the information, compute two-tailed test statistics (0.5’).
- Then, make the decision whether you can reject the null hypothesis and justify your decision (0.5’).
- Lastly, interpret the result (0.5’).
- The dataset provided includes 184 US cities. 21 variables in the dataset, contain information ranging from city sustainability policy actions to population health status, along with local demographic information. The explanation for each variable is on sheet 2. (3’)

Given the information in the dataset, pick one from three research questions and answer the following questions:

- Does cities with higher rate on ease of cycling have higher level of bike usage?
- Does the city with higher level biking usage have less people diagnosed with physical health problems?
- Whether is there a significant difference between cities implementing policy to expand biking/walking trails and cities not expanding biking/walking trails in the proportion of population who are diagnosed with mental health problem?
- Based upon the research question you picked, what is the dependent variable? What is the independent variable?
- What is the measurement level of the dependent variable and independent variable?
- Based upon your research question, please write down the null hypothesis and
**one tailed**alternative hypothesis.