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3. Simple Testing
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Let X1. .... Xn bei.i.d. &gt;(8, 1) . Consider testing
Ho : 0 =0 v.s. H1 :0=1.
(a)
2 points possible (graded)
What would a Type 1 error be in this test?
ORejecting Ho when 8=0
ONot Rejecting Ho when 0=0
ORejecting Ho when 8 = 1
Not rejecting Ho when e = 1
What would a Type 2 error be in this test?
ORejecting Ho when 0=0
ONot Rejecting Ho when 0=0
ORejecting Ho when 0 = 1
Not rejecting Ho when e = 1
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(b)
1 point possible (graded)
Suppose that the rejection region of a test w has the form R = (X, : Xn &gt; c) . Find the smallest
c such that w has level a.
(If applicable, type abs(x) for |x|, Phi(x) for @(x) = P(Z x) where Z ~ N(0, 1) , and q(alpha)
for qu, the 1 - a quantile of a standard normal variable.)
c2
STANDARD
NOTATION
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(c)
2 points possible (graded)
Suppose that the test w has level a = 0.05 . What is the power of w?
(If applicable, type abs(x) for [x|, Phi(x) for @ (x) = P(Z x) where Z ~ N(0, 1) , and q(alpha)
for qu, the 1 - a quantile of a standard normal variable, e.g. enter q(0.01) for 90.01-)
Power of w:
What does the power of w approach as n - co ?
lim Power =

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