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creativ13 [48]
3 years ago
12

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.
Mathematics
1 answer:
Finger [1]3 years ago
6 0

Answer:

C.I. =  (2.297, 11.703)

Step-by-step explanation:

The t-statistic for difference of mean is given by,

t=\frac{\bar{x_{1}}-\bar{x_{2}}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}

Here, \bar{x_{1}} = 84

\bar{x_{2}} = 7

s₁ = 4

n₁ = 12

s₂ = 6

n₂ = 18

Substituting all value in formula,

We get, t = -3.541 at 28 degree of freedom.

Using this formula, we get, t = 1.5342

Therefore, based on the data provided, the 99% confidence interval for the difference between the population means \bar{x_{1}}-\bar{x_{2}} is: 2.297 < \bar{x_{1}}-\bar{x_{2}} < 11.703

which indicates that we are 99% confident that the true difference between population means is contained by the interval (2.297, 11.703)

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