6. Frustrated passengers, congested streets, time schedules, and air and noise pollution are just some of the physical and social pressures that lead many urban bus drivers to retire prematurely with disabilities such as coronary heart disease and stomach disorders. An intervention program designed by the Stockholm Transit District was implemented to improve the work conditions of the city's bus drivers. Improvements were evaluated by collecting physiological and psychological data for bus drivers who drove on the improved routes (intervention) and for drivers who were assigned the normal routes (control). They found a sample mean heart rate and sample standard deviation for the 10 bus drivers in the intervention group of 67.90 and 5.49. Similarly, they found a sample mean heart rate and sample standard deviation for the 31 bus drivers in the control group of 66.81 and 9.04. 1. At the 5% level, test whether the data provide sufficient evidence to conclude that the intervention program reduces mean heart rate of urban bus drivers in Stockholm using the pvalue approach. 2. Find the power of the test in (a) if the true standard deviations for intervention and control are 5.5 and 9.0 respectively, and the true mean difference is -0.8. 3. Suppose we wanted to conduct a test, with two times more bus drivers in the control group than in the intervention group, where the power of the test described in (a) and (b) is 0.9. What sample sizes would be needed for the two groups?