Two distinct solid fuel propellants, type A and type B, are being considered for a space program activity. Burning rates of the propellant are crucial. Random samples of 12 specimens of propellant A are taken with sample means of 84 cm/sec with a standard deviation of 4. And, random samples of 18 specimens of propellant B are taken with sample means of 77 cm/sec with a standard deviation of 6. Find a 99% confidence interval for the difference between the average burning rates for the two propellants. Assume the populations to be approximately normally distributed with equal variances.

Answer:C.I. =  (2.297, 11.703)Step-by-step explanation:The t-statistic for difference of mean is given by,[tex]t=\frac{\bar{x_{1}}-\bar{x_{2}}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}[/tex]Here, [tex]\bar{x_{1}}[/tex] = 84[tex]\bar{x_{2}}[/tex] = 7s₁ = 4n₁ = 12s₂ = 6n₂ = 18Substituting all value in formula,We get, t = -3.541 at 28 degree of freedom.Using this formula, we get, t = 1.5342Therefore, based on the data provided, the 99% confidence interval for the difference between the population means [tex]\bar{x_{1}}-\bar{x_{2}} [/tex] is: 2.297 < [tex]\bar{x_{1}}-\bar{x_{2}} [/tex] < 11.703which indicates that we are 99% confident that the true difference between population means is contained by the interval (2.297, 11.703)