Show that the F distribution with 4 and 4 degrees of freedom is given by
And use this density to find the probability that for independent random samples of size n = 5 from normal populations with the same variance, S21 / S22 will take on a value less than 1/2 or greater than 2.
Answer to relevant QuestionsVerify the results of Example 8.4, that is, the sampling distributions of Y1, Yn, and X~ shown there for random samples from an exponential population. If the first n1 random variables of Exercise 8.2 have Bernoulli distributions with the parameter θ1 and the other n2 random variables have Bernoulli distributions with the parameter θ2, show that, in the notation of ...Use the result of Exercise 8.54 to find the sampling distribution of R for random samples of size n from the continuous uniform population of Exercise 8.46. For random samples from an infinite population, what happens to the standard error of the mean if the sample size is (a) Increased from 30 to 120; (b) Increased from 80 to 180; (c) Decreased from 450 to 50; (d) decreased ...Independent random samples of sizes n1 = 30 and n2 = 50 are taken from two normal populations having the means µ1 = 78 and µ2 = 75 and the variances σ21 = 150 and σ22 = 200. Use the results of Exercise 8.3 to find the ...
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