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.

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JeanaShupp JeanaShupp · Answer 1 · 2019-08-23T11:06:29+02:00

Answer: [tex]z_{\text{calc}}=-0.32[/tex]

Explanation:

The test statistic for difference of two population means :-

[tex]z=\dfrac{\mu_1-\mu_2}{\sigma\sqrt{\dfrac{1}{n_1}+\dfrac{1}{n_2}}}[/tex]

Given : [tex]\sigma=\sigma_1=\sigma_2=3[/tex]

[tex]n_1 = n_2 = 20[/tex]

[tex]\mu_1=23.7[/tex]

[tex]\mu_2=24[/tex]

Then , [tex]z=\dfrac{23.7-24}{(3)\sqrt{\dfrac{1}{20}+\dfrac{1}{20}}}[/tex]

[tex]\Rightarrow\ z=-0.316227766017\approx-0.32[/tex]

Hence, the value of [tex]z_{\text{calc}}=-0.32[/tex]