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If T is a statistic that is approximately normally distributed under the null hypothesis, the next step in performing a Z-test is to estimate the expected value θ of T under the null hypothesis, and then obtain an estimate s of the standard deviation of T. We then calculate the standard score Z = ( T − θ ) / s, from which one-tailed and two-tailed p-values can be calculated as Φ (−| Z |) and 2Φ (−| Z |), respectively, where Φ is the standard normal cumulative distribution function.
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If and T
If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.
If we try to study T using characteristic values, we are confronted with two problems.
If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.
If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.
If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.
If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.
If T is the total `` length '' of the process, its feed state may be denoted by a vector p(T) and the product state by p(Q).
* If S and T are in M then so are S ∪ T and S ∩ T, and also a ( S ∪ T )
* If S and T are in M with S ⊆ T then T − S is in M and a ( T − S ) =
* If a set S is in M and S is congruent to T then T is also in M and a ( S )
* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )
If T is a good symmetry of the dynamics, then
If and is
If the circumstances are faced frankly it is not reasonable to expect this to be true.
If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.
If it is an honest feeling, then why should she not yield to it??
If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.
If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.
If he is good, he may not be legal ; ;
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If the existent form is to be retained new factors that reinforce it must be introduced into the situation.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If he is a traditionalist, he is an eclectic traditionalist.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.
If and statistic
If the list is a statistical sample, we call the resulting statistic a sample mean.
If one chooses a critical value of the test statistic D < sub > α </ sub > such that P ( D < sub > n </ sub > > D < sub > α </ sub >)
If there exists a minimal sufficient statistic, and this is usually the case, then every complete sufficient statistic is necessarily minimal sufficient ( note that this statement does not exclude the option of a pathological case in which a complete sufficient exists while there is no minimal sufficient statistic ).
If X < sub > 1 </ sub >, ...., X < sub > n </ sub > are independent and uniformly distributed on the interval, then T ( X ) = max ( X < sub > 1 </ sub >, …, X < sub > n </ sub >) is sufficient for θ — the sample maximum is a sufficient statistic for the population maximum.
If the parameter space for p is ( 0, 1 ), then T is a complete statistic.
If the sample evidence obtained through x-bar equals − 200 and the corresponding t-test statistic equals − 50, the conclusion from the test would be that there is no evidence that the new treatmnent is better than the existing one: it would not report that it is markedly worse, but that is not what this particular test is looking for.
If the null hypothesis is true ( i. e., men and women are chosen with equal probability in the sample ), the test statistic will be drawn from a chi-squared distribution with one degree of freedom.
If n is sufficiently large, the above binomial distribution may be approximated by a Gaussian ( normal ) distribution and thus the Pearson test statistic approximates a chi-squared distribution,
If the statistic is a percentage, this maximum margin of error can be calculated as the radius of the confidence interval for a reported percentage of 50 %.
If the statistic is a percentage, this maximum margin of error can be calculated as the radius of the confidence interval for a reported percentage of 50 %.
If a relief pitcher satisfies all of the criteria for a save, except he does not finish the game, he will often be credited with a hold ( which is not an officially recognized statistic by Major League Baseball ).
If there are n data points to estimate parameters of both models from, then one can calculate the F statistic ( coefficient of determination ), given by
If the variation of the test statistic is strongly non-normal, a Z-test should not be used.
If the conditioning statistic is both complete and sufficient, and the starting estimator is unbiased, then the Rao – Blackwell estimator is the unique " best unbiased estimator ": see Lehmann – Scheffé theorem.
If the process is in control ( and the process statistic is normal ), 99. 7300 % of all the points will fall between the control limits.
If the test statistic is sufficiently small, the pixel is added to the region, and the region ’ s mean and scatter are recomputed.
If independence is not satisfied, then the average may not actually be a better statistic but may merely reflect the correlations among the individual measurements and their non-independent nature.
If the calculated statistic is outside of the critical value, then you reject the null hypothesis and are forced to accept the alternate hypothesis.
# If the statistic is not significant, then there is no evidence of differences between the samples.
If you have children or you are under the age of 20, then you will be considered in that statistic.
If are k independent, normally distributed random variables with means and standard deviations, then the statistic
If the observations are collected from a random sample, statistical theory provides probabilistic estimates of the likely size of the sampling error for a particular statistic or estimator.
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