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Incentives to Exercise: What Works Best? A study' was designed to see what type of incentive might be most effective in encouraging people to exercise. The goal for each of the overweight participants in the study was to walk 7000 steps a day. The study lasted 100 days and the number of days that each participant met the goal was recorded. The participants were randomly assigned to one of four different incentive groups: for each day they met the goal, participants in the first group got only an acknowledgement, participants in the second group got entered into a lottery, and participants in the third group received cash (about $1.50 per day). In the fourth group, participants received all the money up front and lost money (about $1.50 per day) if they didn't meet the goal. The success rate was almost identical in the first three groups (in other words, giving cash did not work much better than just saying congratulations) and the mean number of days meeting the goal for these participants was 33.7. For the participants who would lose money, however, the mean number of days meeting the goal was 45.0. (People really hate to lose money!) Test to see if this provides evidence of a difference in means between those losing money and those with other types of incentives, using the fact that the standard error for the difference in means is 4.14. Let group 1 be the people in a 100-day program to encourage exercise who lose money and let group 2 be people in a 100-day program to encourage exercise given other types of incentives. 1Patel MS, et al., "Framing Financial Incentives to Increase Physical Activity Among Overweight and Obese Adults: A Randomized, Controlled Trial," Annals of Internal Medicine, 2016; 164(6):385-394.X Your answer is incorrect. What is the test statistic? Round your answer to three decimal places. HI 4.830 eTextbook and Media Hint Assistance Used X Your answer is incorrect. What is the p-value? Round your answer to four decimal places. p-value = 0.549Smoke-Free Legislation and Asthma Hospital admissions for asthma in children younger than 15 years was studied in Scotland both before and after comprehensive smoke-free legislation was passed in March 2006. Monthly records were kept of the annualized percent change in asthma admissions, both before and after the legislation was passed. For the sample studied, before the legislation, admissions for asthma were increasing at a mean rate of 5.2% per year. The standard error for this estimate is 0.7% per year. After the legislation, admissions were decreasing at a mean rate of 18.2% per year, with a standard error for this mean of 1.79%. In both cases, the sample size is large enough to use a normal distribution. 1Mackay, D., et. al., "Smoke-free Legislation and Hospitalizations for Childhood Asthma," The New England Journal of Medicine, September 16, 2010; 363(12):1139-45. X Your answer is incorrect. (a) Find a 95% confidence interval for the mean annual percent rate of change in childhood asthma hospital admissions in Scotland before the smoke-free legislation. Round your answers to one decimal place. The 95% confidence interval is i 16.41 % to 7.0 % .X Your answer is incorrect. (b) Find a 95% confidence interval for the same quantity after the legislation. Round your answers to one decimal place. The 95% confidence interval is i 13.1 % to 22.8 %