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 σ1 = σ 2 = 3 centimeters per second. Two random samples of n1 = 20 and n2 = 20 specimens are tested; the sample mean burning rates are = 18 centimeters per second and = 24 centimeters per second.
(a) Test the hypothesis that both propellants have the same mean burning rate. Use α = 0.05.
(b) What is the P-value of the test in part (a)?
(c) What is the β-error of the test in part (a) if the true difference in mean burning rate is 2.5 centimeters per second?
(d) Construct a 95% confidence interval on the difference in means μ1 – μ2. What is the practical meaning of this interval?