please make the answer clear

1. A certain type of automobile is known to sustain no visible damage 25% of the time in 10-mph crash tests. A modified bumper design has been proposed in an effort to increase this percentage. Let p denote the proportion of all 10-mph crashes with this new bumper that will result in no visible damage. The hypotheses to be tested are Ho : p = .25 versus HA : p > .25. The test will be based on an experiment involving n = 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 S for different values in the alternative: .3,.4, .5, .6, .7, .8. (b) Calculate a for the rejection region {Y 2 9} and calculate S for different values in the alternative: .3,.4, .5, .6, .7, .8. (c) Compare the results in (a) with those in (b). 2. Let u denote the true average tread life of a certain type of tire. Consider testing Ho : A = 20, 000 versus H, : / > 20, 000 based on a sample of size n = 16 from a normal population distribution with o = 1500. (a) What is the rejection region for a significance level of a = 0.01? (b) What is the probability of making a type II error when / = 21, 000