Let Y 1 follow a normal distribution with mean 50 and variance 12. Let Y 2 follo

Question

Let Y1 follow a normal distribution with mean 50 and variance 12. Let Y2 follow a normal distribution with mean 60 and variance 9. A random sample of size 4 is drawn from Y1 and another independent random sample of size 9 is drawn from Y2. Let sample mean of the first sample be denoted by M1 and sample mean of the second sample be denoted M2. Then Z = M1 - M2 follows a normal distribution

A. mean 10 and standard deviation 2

B. mean -10 and standard deviation 2

C. mean -10 and standard deviation 2

D. mean 10 and standard deviation 2

E. None of the above

Explanation / Answer

The mean of Z = M1 - M2 = Y1bar - Y2bar = 50 - 60 = -10.

The standard deviation of their difference is

s(M1 - M2) = sqrt(var1/n1 + var2/n2)

Thus,

s(M1 - M2) = sqrt(12/4 + 9/9) = sqrt(4) = 2.

Thus, the answer is OPTION B: mean = -10, standard deviation = 2. [ANSWER]

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