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