Consider two different normal distributions for which both the means 1 and 2 and the variances 21 and 22 are unknown, and suppose that it is desired to test the following hypotheses H0 21 22, H1 21 22 Suppose further that a random sample consisting of 16 observations for the first normal distribution yields the values 563, and an independent random sample consisting of 10 observations from the second normal distribution yields the values and a What are the M L E s of 21 and 22 b If an F test is carried out at the level of significance 0 05, is the hypothesis H0 rejected or not

Question: Consider two different normal distributions for which both the means 1 and 2 and the variances 21 and 22 are unknown, and suppose that it

Consider two different normal distributions for which both the means μ1 and μ2 and the variances σ21 and σ22 are unknown, and suppose that it is desired to test the following hypotheses:
H0: σ21 ≤ σ22,
H1: σ21 > σ22.
Suppose further that a random sample consisting of 16 observations for the first normal yields the values = 563, and an independent random sample consisting of 10 observations from the second normal yields the values
and
a. What are the M.L.E.’s of σ21 and σ22?
b. If an F test is carried out at the level of significance 0.05, is the hypothesis H0 rejected or not?

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