Let F be a random variable with the Fn,m distribution and G be a random variable

Question

Let F be a random variable with the Fn,m distribution and G be a random variable with the Fm,n distribution. If P(G < x) = p then P(F > 1/x) = p.
Suppose that X N(µx,2 x) and Y N(µy,2 y). Let X1,...,X7 be an independent random sample from X, with sample variance S2 x and Y1,...,Y8 be an independent random sample from Y , with sample variance S2 y.

a) Find a value b such that
P(F6,7 < b) = 0.975.

b) Find a value a such that
P(F6,7 > a) = 0.975.

c) Hence, if S2 x = 3.6 and S2 y = 5.2, compute a 95% condence interval for 2 x/2 y.

d) Is there sucient evidence to suggest 2 x 6= 2 y?

Explanation / Answer

a)

b = 5.118597

b)

a = 0.175578

c)

95% Confidence Intervals

                            CI for
         CI for StDev      Variance
Method       Ratio           Ratio
F       (0.368, 1.986) (0.135, 3.943)

d)

since 1 is present in confidence interval,there is not sucient evidence to suggest 2 x 6= 2 y

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