2. For this question, you can make use a statistical package (such as STATA or R) or the online power calculator at https://clincalc.com/stats/power.aspx. You plan to run an experiment in which you incentivize people to walk. You randomly allocate 50 people to the control group (no incentives) and 50 to the treatment group (incentives). You expect that people in the control group will on average walk 7,500 steps a day with a standard deviation of 3,500, and in the treatment group 9,000 steps a day with a standard deviation of 3,500. a. Use the online calculator to determine the power of your study. As inputs you can use the following: You have two independent samples, the outcome is continuous, and the significance level is set to 5% (alpha=.05). Use a two-sided test (the default). b. If you want to reach a power of 80%, how many subjects would you need in each treatment? c. If you have 50 people in each treatment, and people in the control group walk on average 7,500 steps, how large should the treatment effect be to reach a power of 80%? d. Assume now that the standard deviation in the treatment group is 6,000 instead of 3,500. Calculate the power if you have 50 people in each group. Compare your answer to your answer under (a). e. Assume again a standard deviation of 6,000 in the treatment group. Calculate the power if you have 40 people in the control group and 60 people in the treatment group. Compare your answer to your answer under (d).