Question

The combustion rate of two solid propellants that are used in exhaust systems is studied emergency of airplanes. It is known that the combustion rate of the two propellants is distributed normally with standard deviations σ1 = 3 cm / s and σ2 = 2.9 cm / s. Two samples are tested size 20 random samples, one for each propellant, and the resulting sample means for the rate of combustion are: x̅̅1̅ = 18 cm / s and x̅̅2̅ = 24 cm / s.

a) Test the hypothesis that the two solid propellants provide the same combustion rate average using a level of significance of 5%.

b) Determine the P value of the test in a).

c) Determine the power of the test (1-β) in a) if the true difference in the average rate of combustion is 4.5 cm / s. Use a level of significance of 5% and estimate the population variances through the sample variances.

d) Test the hypothesis that the difference in the average combustion rate of the two propellants is greater than 4, using a level of significance of 5%.

e) Determine the power of the test in d) if the true difference in the average combustion rate it is 4.5 cm / s. Estimate the population variances through the sample variances and use a level of significance of 5%.

Answer 1