Question

The burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. It is known that both propellants have the same standard deviation of burning rate; σ1 = σ2 = 3 centimetres per second. Two random samples of n1 = n2 = 20 are tested; the sample mean burning rates are 21 and 24 centimetres per second respectively.

Construct a 95% upper bound on the difference in means μ1 − μ2. Answer to two decimal places please.

Answer 1

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(9/20 + 9/20)
sp = 0.9487

Given CI level is 0.95, hence α = 1 - 0.95 = 0.05                  
α/2 = 0.05/2 = 0.025, zc = z(α/2, df) = 1.96                  
                  
Margin of Error                  
ME = zc * sp                  
ME = 1.96 * 0.9487                  
ME = 1.859                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (21 - 24 - 1.96 * 0.9487 , 21 - 24 - 1.96 * 0.9487                  
CI = (-4.86 , -1.14)  

upper bound = -1.14