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β error of the test and determination of sample size to obtain power.

The burning rates of 2 different solid-fuel propellants used in aircrew escape systems are being studied. It is known that both propellants have approximately the similar standard deviation of burning rate, that is σ1=σ2=3 centimeters per second. Two random samples of n1=20 and n2=20 specimens are tested, the sample mean burning rates are 1=18 centimeters per second and 2=24 centimeters per second.

a) What is the β-error of the test in part (a) if the true differenc e in mean burning rate is 2.5 centimeters per second?

b) Assume equal sample sizes, what sample size is needed to obtain power of 0.9 at a true difference in means of 14cm/s?

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