Let X have one of the following distributions: X H0 HA x1 .2 .1 x2 .3 .4 x3 .3 .1 x4 .2 .4 a. Com...
Let X have one of the following distributions:
X H0 HA
x1 .2 .1
x2 .3 .4
x3 .3 .1
x4 .2 .4
a. Compare the likelihood ratio, , for each possible value X and
order the xi
according to .
b. What is the likelihood ratio test of H0 versus HA at level α =
.2? What is the
test at level α = .5?
c. If the prior probabilities are P(H0) = P(HA), which outcomes
favor H0?
d. What prior probabilities correspond to the decision rules with α
= .2 and
α = .5?
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Let X have one of the following distributions: X H0 HA x1 .2 .1 x2 .3 .4 x3 .3 .1 x4 .2 .4 a. Com...
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Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2
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2 > 0 is
unknown. Consider testing
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2
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2
0
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For the data x1 = -1, x2 =
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1, x5 = 0,
find ∑
(xi2).
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1 Let X1, X2, X3 be a random sample from a population with density otherwise. What is the form of best critical region of α-0034 for testing Ho : θ 1 versus Ha : θ-27(Hint: You may use the fact that-2(1 + θ)Σ1nKi ~ χ"(6) for finding k)
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Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t...
For the data x1 = -1, x2 =
-3, x3 = -2, x4 =
1, x5 = 0,
find ∑
(xi2).
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