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 23.7 and 24 centimetres per second respectively. If you want to test the hypothesis that the burning rates of the 2 propellants are different, what is the value of zcalc? In computing zcalc, use the hypothesis test with respect to LaTeX: \mu1-\mu2 μ 1 − μ 2 . Please report your answer in 2 decimal places.

Answer 1

Answer: $z_{\text{calc}}=-0.32$

Explanation:

The test statistic for difference of two population means :-

$z=\dfrac{\mu_1-\mu_2}{\sigma\sqrt{\dfrac{1}{n_1}+\dfrac{1}{n_2}}}$

Given : $\sigma=\sigma_1=\sigma_2=3$

$n_1 = n_2 = 20$

$\mu_1=23.7$

$\mu_2=24$

Then , $z=\dfrac{23.7-24}{(3)\sqrt{\dfrac{1}{20}+\dfrac{1}{20}}}$

$\Rightarrow\ z=-0.316227766017\approx-0.32$

Hence, the value of $z_{\text{calc}}=-0.32$