The burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. it is known that both propellants have approximately the same standard deviation of burning rate; that is sigma 1 equals sigma 2 equals 4 centimeters per second. two random samples of n 1 equals 20 and n 2 equals 20 specimens are tested; the sample mean burning rates are x overbar subscript 1 baseline equals 17 centimeters per second and x overbar subscript 2 baseline equals 25 centimeters per second. (a) test the hypothesis that both propellants have the same mean burning rate. use what is the p-value? (b) construct a 95% confidence interval on the difference in means (c) what is the beta-error of the test in part (a) if the true difference in mean burning rate is 2.5 centimeters per second? (d) assuming equal sample sizes, what sample size is needed to obtain power of 0.9 at a true difference in means of 4 cm/s?