Question

Air crew escape systems are powered by a solid propellant. The burning rate of this propellant is an important product characteristic. Specifications require that the mean burning rate must be 50 centimeters per second. The experimenter selects a random sample of and obtains an observed sample mean of the burning rate 51.3 centimeters per second and an observed sample standard deviation of the burning rate 2.0 centimeters per second. Based on a 5% type I error threshold, construct a hypothesis test and draw your conclusion.

Answer 1

Answer:

Step-by-step explanation:

Hello!

The objective is to test if the mean burning rate of a propellant follows the specificated 50 cm/s.

The variable of interest is X: burning rate of a propellant (cm/s)

A sample of n= 25 was taken and a sample mean X[bar]= 51.3 cm/s and a sample standard deviation S= 2.0 cm/s were obtained.

Assuming that the variable has a normal distribution, the parameter of interest is the population mean, and the statistic hypotheses are:

H₀: μ = 50

H₁: μ ≠ 50

α: 0.05

Since there is no information about the population variance and the variable has a normal distribution the statistic to choose is a one-sample t-test:

$t_{H_0}= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } = \frac{51.3-50}{\frac{2.0}{\sqrt{25} } } = 3.25$

The p-value corresponding to this test is p-value 0.003402

The decision for deciding using the p-value is:

If p-value ≤ α ⇒ Reject the null hypothesis.

If p-value > α ⇒ Not reject the null hypothesis.

The p-value is less than the significance level, the decision is to reject the null hypothesis. Using a level of significance of 5% you can conclude that the population mean burning rate of propellant is not 50 cm/s.

I hope it helps!