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?