1. A certain type of automobile is known to sustain no visible damage 25% of the time in 10mph crash tests. A modied bumper design has been proposed in an effort to increase this percentage. Let p denote the proportion of all 10mph crashes with this new bumper that will result in no visible damage. The hypotheses to be tested are H) 2 'p = .25 versus H A : p > .25. The test will be based on an experiment involving 71 = 20 independent crashes with prototypes of the new design. Let Y = number of crashes with no visible damage. (a) Calculate a for the rejection region {Y 2 8} and calculate 6 for different values in the alternative: .3,.4, .5, .6, .7, .8. (b) Calculate a for the rejection region {Y 2 9} and calculate for different values in the alternative: .3,.4, .5, .6, .7, .8. (0) Compare the results in (a) with those in (b)