Luis A. Afonso
Posts:
4,275
From:
LIsbon (Portugal)
Registered:
2/16/05
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Re: More dumb question on hypothesis-testing: Symmetry of Ha.?. Sample size.?
Posted:
Dec 9, 2010 3:51 AM
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The Logic Behind Hypotheses Tests
Testing the value of a parameter m in comparison with a real number m0.
TWO TAIL´s TEST
H0 : m = m0______Ha : m =/ m0
Let be F(Z | H0) the Distribution Function of the test and alpha (ordinarily = 0.05) a preset Significance Level (SL). The Confidence Interval (CI) relative to alpha is bounded by two quantities left, right , the critical values, CV, such that
F( Z= left | H0) = alpha/2
F( Z= right | H0) = 1 - alpha/2
In consequence, from the interval CI = [ left , right ] , the conclusions are got:
If the test value Z0 is inside (bounds included) CI one have no sufficient evidence to reject H0, on contrary if Z0 < left OR Z0 > right then H0 is rejected, the parameter m is not equal to m0.
ONE TAIL TEST
RIGHT
H0 : m < = m0________Ha : m > m0
This time the CI = ( ?infinity, CV ] where
F( Z= CV | H0) = alpha and one conclude that there is not sufficient evidence to reject H0 if Z0 is inside CI, which is the same thing to say that Z0 <= CV. Alternatively when Z0 is outside CI then H0 is rejected: the parameter m is greater than the real quantity m0 (Z0 > CV).
LEFT
H0: m >= m0_________Ha : m < m0
CI = [CV , + infinity) the *acceptance interval*, better saying: not rejection interval. We must reject H0 if Z < CV.
Luis
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