The burning rates of two different solid-fuel propellants usedin aircrew escape systems are being studied. it is known that bothpropellants have approximately the same standard deviation ofburning rate; that is α1 = α 2 = 3 centimeters persecond. two random samples of n1 = 20 and n2 = 20 specimensare tested; the sample mean burning rates are 1 = 18 centimeters per second and 2 = 24 centimeters per second.
(a) test the hypothesis that both propellants have the samemean burning rate. use α= 0.05. what is thep-value?
(b) contruct a 95% confidence interval on the difference inmean s μ1 - μ2. what is the practical meaning of thisinterval?
(c) what is the β-error of the test in part (a) if thetrue difference in mean burning rate is 2.5 centimeters persecond?
(d) assuming equal sample sizes, what sample size is needed toobtain power of 0.9 at a true deifference in means of14cm/s?