The burning rates of two different solid-fuel propellants used in air crew escape systems are being studied. A random sample of 15 first type propellants are tested resulting in a sample mean burning rate of 18 cm/s and sample standard deviation of 2.75 cm/s. Another sample of 15 second type propellants are tested resulting in a sample mean burning rate of 24 cm/s and sample standard deviation of 2.80 cm/s. Assume both populations are independent and normally distributed and have the equal but unknown variances.
(a) (10 pts) Is there sufficient evidence to claim that the mean burning rate of the first type propellant is less than that of the second type propellant at α = 0.05? Use fixed significance level approach to answer this question.
(b) (8 pts) Construct an appropriate confidence interval to answer question in part (a).
(c) (4 pts) Without doing any calculation or looking up a table, can you figure out whether P-value is greater than 0.05? Why or why not?